Showing papers on "Ising model published in 1999"

Bosonization and Strongly Correlated Systems

Abstract: This volume provides a detailed account of bosonization. The first part of the book examines the technical aspects of bosonization including one-dimensional fermions, the Gaussian model, the structure of Hilbert space in conformal theories, Bose-Einstein condensation in two dimensions, non-Abelian bosonization, and the Ising and WZNW models. The second part presents applications of the bosonization technique to realistic models including the Tomonaga-Luttinger liquid, spin liquids in one dimension and the spin-1/2 Heisenberg chain with alternative exchange. The third part addresses the problems of quantum impurities. Chapters cover potential scattering, the X-ray edge problem, impurities in Tomonaga-Luttinger liquids and the multi-channel Kondo problem.

Lectures on Glauber dynamics for discrete spin models

Abstract: These notes have been the subject of a course I gave in the summer 1997 for the school in probability theory in Saint-Flour. I review in a self-contained way the state of the art, sometimes providing new and simpler proofs of the most relevant results, of the theory of Glauber dynamics for classical lattice spin models of statistical mechanics. The material covers the dynamics in the one phase region, in the presence of boundary phase transitions, in the phase coexistence region for the two dimensional Ising model and in the so-called Griffiths phase for random Systems.

Conformal Invariance and Critical Phenomena

Abstract: 1. Critical Phenomena: a Reminder.- 2. Conformal Invariance.- 3. Finite-Size Scaling.- 4. Representation Theory of the Virasoro Algebra.- 5. Correlators, Null Vectors and Operator Algebra.- 6. Ising Model Correlators.- 7. Coulomb Gas Realization.- 8. The Hamiltonian Limit and Universality.- 9. Numerical Techniques.- 10. Conformal Invariance in the Ising Quantum Chain.- 11. Modular Invariance.- 12. Further Developments and Applications.- 13. Conformal Perturbation Theory.- 14. The Vicinity of the Critical Point.- 15. Surface Critical Phenomena.- 16. Strongly Anisotropic Scaling.- Anhang/Annexe.- List of Tables.- List of Figures.- References.

Persistence in nonequilibrium systems

Abstract: THE problem of persistence in spatially extended nonequilibrium systems has recently generated a lot of interest both theoretically and experimentally. Persistence is simply the probability that the local value of the fluctuating nonequilibrium field does not change sign up to time t. It has been studied in various systems, including several models undergoing phase separation, the simple diffusion equation with random initial conditions, several reaction diffusion systems in both pure and disordered environments, fluctuating interfaces, Lotka–Volterra models of population dynamics, and granular media. The precise definition of persistence is as follows. Let φ(x, t) be a nonequilibrium field fluctuating in space and time according to some dynamics. For example, it could represent the coarsening spin field in the Ising model after being quenched to low temperature from an initial high temperature. It could also be simply a diffusing field starting from random initial configuration or the height of a fluctuating interface. Persistence is simply the probability P0(t) that at a fixed point in space, the quantity sgn[φ(x, t) – 〈φ(x, t)〉] does not change up to time t. In all the examples mentioned above this probability decays as a power law P0(t) ~ t –θ at late times, where the persistence exponent θ is usually nontrivial. In this article, we review some recent theoretical efforts in calculating this nontrivial exponent in various models and also mention some recent experiments that measured this exponent. The plan of the paper is as follows. We first discuss the persistence in very simple single variable systems. This makes the ground for later study of persistence in more complex many-body systems. Next, we consider many-body systems such as the Ising model and discuss where the complexity is coming from. We follow it up with the calculation of this exponent for a simpler manybody system namely diffusion equation and see that even in this simple case, the exponent θ is nontrivial. Next, we show that all these examples can be viewed within the general framework of the ‘zero crossing’ problem of a Gaussian stationary process (GSP). We review the new results obtained for this general Gaussian problem in various special cases. Finally, we mention the emerging new directions towards different generalizations of persistence. We start with a very simple system namely the onedimensional Brownian walker. Let φ(t) represent the position of a 1-D Brownian walker at time t. This is a single-body system in the sense that the field φ has no x dependence but only t dependence. The position of the walker evolves as,

A Discrete Convolution Model¶for Phase Transitions

Abstract: We study a discrete convolution model for Ising-like phase transitions. This nonlocal model is derived as an l 2-gradient flow for a Helmholtz free energy functional with general long range interactions. We construct traveling waves and stationary solutions, and study their uniqueness and stability. In particular, we find some criteria for “propagation” and “pinning”, and compare our results with those for a previously studied continuum convolution model.

Phase behavior of the restricted primitive model and square-well fluids from Monte Carlo simulations in the grand canonical ensemble

Abstract: Coexistence curves of square-well fluids with variable interaction width and of the restricted primitive model for ionic solutions have been investigated by means of grand canonical Monte Carlo simulations aided by histogram reweighting and multicanonical sampling techniques. It is demonstrated that this approach results in efficient data collection. The shape of the coexistence curve of the square-well fluid with short potential range is nearly cubic. In contrast, for a system with a longer potential range, the coexistence curve closely resembles a parabola, except near the critical point. The critical compressibility factor for the square-well fluids increases with increasing range. The critical behavior of the restricted primitive model was found to be consistent with the Ising universality class. The critical temperature was obtained as Tc=0.0490±0.0003 and the critical density ρc=0.070±0.005, both in reduced units. The critical temperature estimate is consistent with the recent calculation of Caillol...

Scaling corrections: Site percolation and Ising model in three-dimensions

Abstract: Using finite-size scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention to parametrizing the corrections-to-scaling, which is necessary to bring the systematic errors below the statistical ones.

Density matrix renormalization : a new numerical method in physics : lectures of a seminar and workshop held at the Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany, August 24th to September 18th, 1998

Abstract: Wilson's numerical renormalization group.- The Density Matrix Renormalization Group.- Thermodynamic limit and matrix-product states.- A recurrent variational approach.- Transfer-matrix approach to classical systems.- Quantum transfer-matrix and momentum-space DMRG.- Calculation of dynamical properties.- Properties of the hubbard chain.- Soliton bound-states in dimerized spin chains.- Haldane phase, impurity effects and spin ladders.- Spin chain properties.- Electronic structure using DMRG.- Symmetrized DMRG method for conjugated polymers.- Conjugated one-dimensional semiconductors.- Strongly correlated complex systems.- Non-hermitian problems and some other aspects.- Walls, wetting and surface criticality.- Critical two-dimensional ising films with fields.- One-dimensional Kondo lattices.- Impurities in spin chains.- Thermodynamics of ferrimagnets.- Thermodynamics of metallic kondo lattices.- Methods for electron-phonon systems.- Disordered one-dimensional fermi systems.

Dimer order with striped correlations in the J 1 -J 2 Heisenberg model

Abstract: Ground state energies for plaquette and dimer order in the $J_1-J_2$ square-lattice spin-half Heisenberg model are compared using series expansion methods. We find that these energies are remarkably close to each other at intermediate values of $J_2/J_1$, where the model is believed to have a quantum disordered ground state. They join smoothly with those obtained from the Ising expansions for the 2-sublattice N\'eel-state at $J_2/J_1 \approx 0.4$, suggesting a second order transition from a N\'eel state to a quantum disordered state, whereas they cross the energy for the 4-sublattice ordered state at $J_2/J_1 \approx 0.6$ at a large angle, implying a first order transition to the 4-sublattice magnetic state. The strongest evidence that the plaquette phase is not realized in this model comes from the analysis of the series for the singlet and triplet excitation spectra, which suggest an instability in the plaquette phase. Thus, our study supports the recent work of Kotov et al, which presents a strong picture for columnar dimer order in this model. We also discuss the striped nature of spin correlations in this phase, with substantial resonance all along columns of dimers.

Structural investigation of the negative-thermal-expansion material ZrW2O8.

Abstract: High-resolution powder diffraction data have been recorded on cubic ZrW2O8 [a = 9.18000 (3) A at 2 K] at 260 temperatures from 2 to 520 K in 2 K steps. These data have confirmed that α-ZrW2O8 has a negative coefficient of thermal expansion, α = −9.07 × 10−6 K−1 (2–350 K). A `parametric' approach to Rietveld refinement is adopted and it is demonstrated that a full anisotropic refinement can be performed at each temperature, despite using a data collection time of only 5 min. Examination of the resulting structural parameters suggests that the origin of the contraction with increasing temperature can be traced straightforwardly to the rigid-body transverse librations of bridging O atoms. α-ZrW2O8 undergoes a phase transition from P213 to Pa3¯ at 448 K that is associated with the onset of considerable oxygen mobility. The phase transition can be described in terms of a simple cubic three-dimensional Ising model. Unusual kinetics are associated with this phase transition. Hysteresis in the cell parameter through the phase transition is the opposite of that normally observed.

Disorder-induced critical phenomena in hysteresis: Numerical scaling in three and higher dimensions

Abstract: We present numerical simulations of avalanches and critical phenomena associated with hysteresis loops, modeled using the zero-temperature random-field Ising model We study the transition between smooth hysteresis loops and loops with a sharp jump in the magnetization, as the disorder in our model is decreased In a large region near the critical point, we find scaling and critical phenomena, which are well described by the results of an $\ensuremath{\epsilon}$ expansion about six dimensions We present the results of simulations in three, four, and five dimensions, with systems with up to a billion spins ${(1000}^{3})$

Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems

Abstract: High-temperature series are computed for a generalized three-dimensional Ising model with arbitrary potential. Three specific "improved" potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are extracted from high-temperature series specialized to improved potentials, achieving high accuracy; our best estimates are gamma=1.2371(4), nu=0.630 02(23), alpha=0.1099(7), eta=0.0364(4), beta=0.326 48(18). By the same technique, the coefficients of the small-field expansion for the effective potential (Helmholtz free energy) are computed. These results are applied to the construction of parametric representations of the critical equation of state. A systematic approximation scheme, based on a global stationarity condition, is introduced (the lowest-order approximation reproduces the linear parametric model). This scheme is used for an accurate determination of universal ratios of amplitudes. A comparison with other theoretical and experimental determinations of universal quantities is presented.

On the singularity structure of the 2D Ising model susceptibility

Abstract: Some simplifications of the integrals (2n+1), derived by Wu et al (1976 13 316), that contribute to the zero field susceptibility of the 2D square lattice Ising model are reported. In particular, several alternate expressions for the integrands in (2n+1) are determined which greatly facilitate both the generation of high-temperature series and analytical analysis. One can show that as series, (2n+1) = 22n(s/2)4n(n+1)(1+O(s)) where s is the high-temperature variable sin(2K) with K the conventional normalized inverse temperature. Analysis of the integrals near symmetry points of the integrands shows that (2n+1)(s) is singular on the unit circle at sk = exp(ik) where 2cos(k) = cos(2 k/(2n+1))+cos(2/(2n+1)), -n k, n. The singularities, k = 0 excepted, are logarithmic branch points of order 2n(n+1)-1ln() with = 1-s/sk. There is numerical evidence from series that these van Hove points, in addition to the known points at s = ?1 and ?i, exhaust the singularities on the unit circle. Barring cancellation from extra (unobserved) singularities one can conclude that |s| = 1 is a natural boundary for the susceptibility.

Critical exponents of the three-dimensional Ising universality class from finite-size scaling with standard and improved actions

Abstract: We compute an improved action for the Ising universality class in three dimensions that has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling constants. We studied three different models: the $\ifmmode\pm\else\textpm\fi{}1$ Ising model with nearest-neighbor and body diagonal interaction, the spin-1 model with states $0,\ifmmode\pm\else\textpm\fi{}1$, and nearest-neighbor interaction, and ${\ensuremath{\varphi}}^{4}$ theory on the lattice (Landau-Ginzburg model). The remarkable finite-size scaling properties of the suitably tuned spin-1 model are compared in detail with those of the standard Ising model. Great care is taken to estimate the systematic errors from residual corrections to scaling. Our best estimates for the critical exponents are $\ensuremath{ u}=0.6298(5)$ and $\ensuremath{\eta}=0.0366(8)$, where the given error estimates take into account the statistical and systematic uncertainties.

The Wulff Construction in Three and More Dimensions

Abstract: In this paper we prove the Wulff construction in three and more dimensions for an Ising model with nearest neighbor interaction.

Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition

Abstract: Hysteresis is studied for a two-dimensional, spin- (1) /(2) , nearest-neighbor, kinetic Ising ferromagnet in a sinusoidally oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on large systems and moderately strong field amplitudes at a temperature below T{sub c}. In this parameter regime, the magnetization switches through random nucleation and subsequent growth of {ital many} droplets of spins aligned with the applied field. Using a time-dependent extension of the Kolmogorov-Johnson-Mehl-Avrami theory of metastable decay, we analyze the statistical properties of the hysteresis-loop area and the correlation between the magnetization and the field. This analysis enables us to accurately predict the results of extensive Monte Carlo simulations. The average loop area exhibits an extremely slow approach to an asymptotic, logarithmic dependence on the product of the amplitude and the field frequency. This may explain the inconsistent exponent estimates reported in previous attempts to fit experimental and numerical data for the low-frequency behavior of this quantity to a power law. At higher frequencies we observe a dynamic phase transition. Applying standard finite-size scaling techniques from the theory of second-order equilibrium phase transitions to this {ital nonequilibrium} transition, we obtain estimates for the transition frequency and the critical exponentsmore » ({beta}/{nu}{approx}0.11,thinsp{gamma}/{nu}{approx}1.84, and {nu}{approx}1.1). In addition to their significance for the interpretation of recent experiments on switching in ferromagnetic and ferroelectric nanoparticles and thin films, our results provide evidence for the relevance of universality and finite-size scaling to dynamic phase transitions in spatially extended nonstationary systems. {copyright} {ital 1999} {ital The American Physical Society}« less

Domain wall theory for ferroelectric hysteresis

Abstract: This paper addresses the modeling of hysteresis in ferroelectric materials through consideration of domain wall bending and translation. The development is considered in two steps. First, dielectric constitutive relations are obtained through consideration of Langevin, Ising spin and preferred orientation theories with domain interactions incorporated through mean field relations. This yields a model for the anhysteretic polarization that occurs in the absence of domain wall pinning. Second, hysteresis is incorporated through the consideration of domain wall dynamics and the quantification of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.

Optimized free-energy evaluation using a single reversible-scaling simulation

Abstract: We present a method, for highly efficient free-energy calculations by means of molecular dynamics and Monte Carlo simulations, which is an optimized combination of coupling parameter and adiabatic switching formalisms. This approach involves dynamical reversible scaling of the potential energy function of a system of interest, and allows accurate determination of its free energy over a wide temperature interval from a single simulation. The method is demonstrated in two applications: crystalline Si at zero pressure and a fcc nearest-neighbor antiferromagnetic Ising model.

First-Order Phase Transition in a Quantum Hall Ferromagnet

Abstract: The single-particle energy spectrum of a two-dimensional electron gas in a perpendicular magnetic field consists of equally-spaced spin-split Landau levels, whose degeneracy is proportional to the magnetic field strength. At integer and particular fractional ratios between the number of electrons and the degeneracy of a Landau level (filling factors n) quantum Hall effects occur, characterised by a vanishingly small longitudinal resistance and quantised Hall voltage. The quantum Hall regime offers unique possibilities for the study of cooperative phenomena in many-particle systems under well-controlled conditions. Among the fields that benefit from quantum-Hall studies is magnetism, which remains poorly understood in conventional material. Both isotropic and anisotropic ferromagnetic ground states have been predicted and few of them have been experimentally studied in quantum Hall samples with different geometries and filling factors. Here we present evidence of first-order phase transitions in n = 2 and 4 quantum Hall states confined to a wide gallium arsenide quantum well. The observed hysteretic behaviour and anomalous temperature dependence in the longitudinal resistivity indicate the occurrence of a transition between the two distinct ground states of an Ising quantum-Hall ferromagnet. Detailed many-body calculations allowed the identification of the microscopic origin of the anisotropy field.

Miscibility behavior and single chain properties in polymer blends : a bond fluctuation model study

Abstract: Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory-Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small-angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb3) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self-consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non-additive monomer shapes, one has a large positive chain-length-independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non-entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End-functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off-lattice simulations and analytical theories are briefly discussed.

Application of a continuous time cluster algorithm to the two-dimensional random quantum Ising ferromagnet

Abstract: A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Griffiths-McCoy phase indicate that the dynamical critical exponent is infinite as in 1d.

Test of the Kolmogorov-Johnson-Mehl-Avrami picture of metastable decay in a model with microscopic dynamics

Abstract: The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory for the time evolution of the order parameter in systems undergoing first-order phase transformations has been extended by Sekimoto to the level of two-point correlation functions. Here, this extended KJMA theory is applied to a kinetic Ising lattice-gas model, in which the elementary kinetic processes act on microscopic length and time scales. The theoretical framework is used to analyze data from extensive Monte Carlo simulations. The theory is inherently a mesoscopic continuum picture, and in principle it requires a large separation between the microscopic scales and the mesoscopic scales characteristic of the evolving two-phase structure. Nevertheless, we find excellent quantitative agreement with the simulations in a large parameter regime, extending remarkably far towards strong fields (large supersaturations) and correspondingly small nucleation barriers. The original KJMA theory permits direct measurement of the order parameter in the metastable phase, and using the extension to correlation functions one can also perform separate measurements of the nucleation rate and the average velocity of the convoluted interface between the metastable and stable phase regions. The values obtained for all three quantities are verified by other theoretical and computational methods. As these quantities are often difficult to measure directly during a processmore » of phase transformation, data analysis using the extended KJMA theory may provide a useful experimental alternative. {copyright} {ital 1999} {ital The American Physical Society}« less

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

Abstract: We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse held. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse held then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRODT and numerical work. [S0163-1829(99)07125-8].

Analytical solution of 1D Ising-like systems modified by weak long range interaction - Application to spin crossover compounds

Abstract: It is well-known that 1D systems with only nearest neighbour interaction exhibit no phase transition. It is shown that the presence of a small long range interaction treated by the mean field approximation in addition to strong nearest neighbour interaction gives rise to hysteresis curves of large width. This situation is believed to exist in spin crossover systems where by the deformation of the spin changing molecules, an elastic coupling leads to a long range interaction, and strong bonding between the molecules in a chain compound leads to large values for nearest neighbour interaction constants. For this interaction scheme an analytical solution has been derived and the interplay between these two types of interaction is discussed on the basis of experimental data of the chain compound [Fe(Htrz)2(trz)](BF4)2 which exhibits a very large hysteresis of 50 K above RT at 370 K. The width and shape of the hysteresis loop depend on the balance between long and short range interaction. For short range interaction energies much larger than the transition temperature κBTt the hysteresis width is determined by the long range interaction alone.

A new perspective on matter coupling in two-dimensional gravity.

Abstract: We provide compelling evidence that a previously introduced model of non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional) flat-space behaviour when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravity-matter system. This weak-coupling behaviour lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions, with a different, and much ‘smoother’ critical behaviour.

Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus

Abstract: Using results from conformal field theory, we compute several universal amplitude ratios for the two-dimensional Ising model at criticality on a symmetric torus These include the correlation-length ratio x^\star = \lim_{L\to\infty} \xi(L)/L and the first four magnetization moment ratios V_{2n} = / ^n As a corollary we get the first four renormalized 2n-point coupling constants for the massless theory on a symmetric torus, G_{2n}^* We confirm these predictions by a high-precision Monte Carlo simulation

Transition from zero-dimensional superparamagnetism to two-dimensional ferromagnetism of co clusters on au(111)

Abstract: The early growth stages of Co structures on Au(111) have been analyzed by scanning tunneling microscopy and their magnetic properties simultaneously measured, in situ, by Kerr effect and, ex situ by superconducting quantum interference device. With increasing cobalt coverage, cobalt clusters, organized on the lattice of the $22\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ zigzag reconstruction coalesce into one-dimensional (1D) chains at a coverage of 1.0 monolayer (ML) and then into a nearly continuous film at 2 ML. While this well-defined growth mode is dictated by the presence of ordered point dislocations at the zigzag reconstruction of the relaxed gold surface, anomalous nucleation and growth is also observed when large domains of strained linear reconstructions are present. Two families of clusters must then be considered with important consequences for magnetic properties. When only the zigzag reconstruction is present, the onset of long-range, 2D ferromagnetism is observed at a coverage of 1.6 ML of cobalt. A Monte Carlo simulation of an anisotropic Heisenberg model describes well transitions from 0D cluster superparamagnetism, to 1D Ising behavior and finally to 2D ferromagnetism as a function of cobalt coverage, in good agreement with experimental results.

Waterlike anomalies for core-softened models of fluids: one dimension.

Abstract: We use a one-dimensional (1D) core-softened potential to develop a physical picture for some of the anomalies present in liquid water. The core-softened potential mimics the effect of hydrogen bonding. The interest in the 1D system stems from the facts that closed-form results are possible and that the qualitative behavior in 1D is reproduced in the liquid phase for higher dimensions. We discuss the relation between the shape of the potential and the density anomaly, and we study the entropy anomaly resulting from the density anomaly. We find that certain forms of the two-step square-well potential lead to the existence at T=0 of a low-density phase favored at low pressures and of a high-density phase favored at high pressures, and to the appearance of a point C' at a positive pressure, which is the analog of the T=0 "critical point" in the 1D Ising model. The existence of point C' leads to anomalous behavior of the isothermal compressibility K(T) and the isobaric specific heat C(P).