Showing papers on "Ising model published in 1998"
TL;DR: In this article, the phase diagram of strongly interacting matter as a function of temperature and baryon number density is explored, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons.
Abstract: We explore the phase diagram of strongly interacting matter as a function of temperature and baryon number density, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons. Our treatment allows us to investigate the possible simultaneous formation of condensates in the conventional quark--anti-quark channel (breaking chiral symmetry) and in a quark--quark channel leading to color superconductivity: the spontaneous breaking of color symmetry via the formation of quark Cooper pairs. At low temperatures, chiral symmetry restoration occurs via a first order transition between a phase with low (or zero) baryon density and a high density color superconducting phase. We find color superconductivity in the high density phase for temperatures less than of order tens to 100 MeV, and find coexisting $ $ and $ $ condensates in this phase in the presence of a current quark mass. At high temperatures, the chiral phase transition is second order in the chiral limit and is a smooth crossover for nonzero current quark mass. A tricritical point separates the first order transition at high densities from the second order transition at high temperatures. In the presence of a current quark mass this tricritical point becomes a second order phase transition with Ising model exponents, suggesting that a long correlation length may develop in heavy ion collisions in which the phase transition is traversed at the appropriate density.
313 citations
TL;DR: The first classification of general types of transition between phases of matter, introduced by Paul Ehrenfest in 1933, lies at a crossroads in the thermodynamical study of critical phenomena as mentioned in this paper.
Abstract: The first classification of general types of transition between phases of matter, introduced by Paul Ehrenfest in 1933, lies at a crossroads in the thermodynamical study of critical phenomena. It arose following the discovery in 1932 of a suprising new phase transition in liquid helium, the “lambda transition,” when W. H. Keesom and coworkers in Leiden, Holland observed a λhaped “jump” discontinuity in the curve giving the temperature dependence of the specific heat of helium at a critical value. This apparent jump led Ehrenfest to introduce a classification of phase transitions on the basis of jumps in derivatives of the free energy function. This classification was immediately applied by A.J. Rutgers to the study of the transition from the normal to superconducting state in metals. Eduard Justi and Max von Laue soon questioned the possibility of its class of “second-order phase transitions” -- of which the “lambda transition was believed to be the arche type -- but C.J. Gorter and H.B.G. Casimir used an “order parameter to demonstrate their existence in superconductors. As a crossroads of study, the Ehrenfest classification was forced to undergo a slow, adaptive evolution during subsequent decades. During the 1940s the classification was increasingly used in discussions of liquid-gas, order-disorder, paramagnetic-ferromagnetic and normal-super-conducting phase transitions. Already in 1944 however, Lars Onsagers solution of the Ising model for two-dimensional magnets was seen to possess a derivative with a logarithmic divergence rather than a jump as the critical point was approached. In the 1950s, experiments further revealed the lambda transition in helium to exhibit similar behavior. Rather than being a prime example of an Ehrenfest phase transition, the lambda transition was seen to lie outside the Ehrenfest classification. The Ehrenfest scheme was then extended to include such singularities, most notably by A. Brain Pippard in 1957, with widespread acceptance. During the 1960s these logarithmic infinities were the focus of the investigation of “scaling” by Leo Kadanoff, B. Widom and others. By the 1970s, a radically simplified binary classification of phase transitions into “first-order” and “continuous” transitions was increasingly adopted.
215 citations
TL;DR: In this paper, Monte Carlo simulations of the short-time critical dynamics are reviewed and the universal scaling behavior of the dynamic Ising model and Potts model are discussed in detail, while extension and application to more complex systems as the XY model, the fully frustrated XY model and other dynamic systems are also presented.
Abstract: Monte Carlo simulations of the short-time critical dynamics are reviewed. The short-time universal scaling behavior of the dynamic Ising model and Potts model are discussed in detail, while extension and application to more complex systems as the XY model, the fully frustrated XY model and other dynamic systems are also presented. The investigation of the universal behavior of the short-time dynamics not only enlarges the fundamental knowledge on critical phenomena but also, more interestingly, provides possible new ways to determine not only the new critical exponents θ and θ1, but also the traditional dynamic critical exponent z as well as all static critical exponents.
185 citations
TL;DR: In this paper, the phase diagram of the site-diluted Ising model in a wide dilution range was studied through Monte Carlo simulations and finite-size scaling techniques.
Abstract: We study the phase diagram of the site-diluted Ising model in a wide dilution range, through Monte Carlo simulations and finite-size scaling techniques. Our results for the critical exponents and universal cumulants turn out to be dilution independent, but only after a proper infinite volume extrapolation, taking into account the leading corrections-to-scaling terms.
174 citations
TL;DR: In this paper, a non-local anisotropic model for phase separation in two-phase fluids at equilibrium is considered, and it is shown that when the thickness of the interface tends to zero in a suitable way, the classical surface tension model is recovered.
Abstract: In this paper we consider a non-local anisotropic model for phase separation in two-phase fluids at equilibrium, and show that when the thickness of the interface tends to zero in a suitable way, the classical surface tension model is recovered. Relevant examples are given by continuum limits of ferromagnetic Ising systems in equilibrium statistical mechanics.
160 citations
TL;DR: In this article, the authors studied hysteresis for a two-dimensional spin-$1/2$ nearest-neighbor kinetic Ising ferromagnet in an oscillating field using Monte Carlo simulations.
Abstract: We study hysteresis for a two-dimensional spin- $1/2$ nearest-neighbor kinetic Ising ferromagnet in an oscillating field using Monte Carlo simulations. The period-averaged magnetization is the order parameter for a proposed dynamic phase transition (DPT). To quantify the nature of this transition, we present the first finite-size scaling study of the DPT for this model. Evidence of a diverging correlation length is given, and we provide estimates of the transition frequency and the critical indices $\ensuremath{\beta}$, $\ensuremath{\gamma}$, and $\ensuremath{
u}$.
160 citations
TL;DR: In this article, the authors used a series of grand canonical Monte Carlo calculations for a small number of state points and combined the results to obtain the phase behavior of a system over a range of temperatures and densities.
Abstract: Histogram reweighting Monte Carlo simulations were used to obtain polymer/solvent phase diagrams for lattice homopolymers of chain lengths up to r = 1000 monomers. The simulation technique was based on performing a series of grand canonical Monte Carlo calculations for a small number of state points and combining the results to obtain the phase behavior of a system over a range of temperatures and densities. Critical parameters were determined from mixed-field finite-size scaling concepts by matching the order parameter distribution near the critical point to the distribution for the three-dimensional Ising universality class. Calculations for the simple cubic lattice (coordination number z = 6) and for a high coordination number version of the same lattice (z = 26) were performed for chain lengths significantly longer than those in previous simulation studies. The critical temperature was found to scale with a chain length following the Flory−Huggins functional form. For the z = 6 lattice, the extrapolat...
159 citations
TL;DR: In this article, the authors compare the behavior of ferromagnetic and antiferromagnetic Ising-type spin models on the cubic pyrochlore lattice, and show that the up-down spin models map onto the in-out spin models with the opposite sign of the exchange coupling.
Abstract: We compare the behaviour of ferromagnetic and antiferromagnetic Ising-type spin models on the cubic pyrochlore lattice. With simple `up - down' Ising spins, the antiferromagnet is highly frustrated and the ferromagnet is not. However, such spin symmetry cannot be realized on the pyrochlore lattice, since it requires a unique symmetry axis, which is incompatible with the cubic symmetry. The only two-state spin symmetry which is compatible is that with four local anisotropy axes, which direct the spins to point in or out of the tetrahedral plaquettes of the pyrochlore lattice. We show how the local `in - out' magnetic anisotropy reverses the roles of the ferro- and antiferromagnetic exchange couplings with regard to frustration, such that the ferromagnet is highly frustrated and the antiferromagnet is not. The in - out ferromagnet is a magnetic analogue of the ice model, which we have termed the `spin ice model'. It is realized in the material . The up - down antiferromagnet is also an analogue of the ice model, albeit a less direct one, as originally shown by Anderson. Combining these results shows that the up - down spin models map onto the in - out spin models with the opposite sign of the exchange coupling. We present Monte Carlo simulations of the susceptibility for each model, and discuss their relevance to experimental systems.
156 citations
TL;DR: In this article, a perturbed sine-Gordon model is used to analyse the evolution of the spectrum of particle excitations in the two-dimensional quantum field theory of a scalar field self-interacting via two periodic terms of frequencies α and β.
139 citations
TL;DR: In this paper, the authors used an Ising model with nearest-neighbour pair interactions to analyze the titration curves of poly(propylene imine) dendrimers at salt concentrations of 0.1, 0.5 and 1.0 M KCl and NaCl.
131 citations
TL;DR: In this article, the authors used Finite-Size Scaling techniques to obtain accurate results for critical quantities of the Ising model and the site percolation, 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 in parameterizing the corrections-to-scaling, what is necessary to put the systematic errors below the statistical ones.
TL;DR: In this paper, a non-perturbative version of the Dobrushin-Kotecký-Shlosman theory of phase separation in the canonical 2D Ising ensemble is presented.
Abstract: We develop a non-perturbative version of the Dobrushin–Kotecký–Shlosman theory of phase separation in the canonical 2D Ising ensemble. The results are valid for all temperatures below critical.
TL;DR: In this article, the authors considered the Glauber dynamics of the infinite volume Ising model in dimension 2 with nearest neighbor ferromagnetic interaction and under a positive external magnetic field h. Minimal conditions on the flip rates are assumed, so that all the common choices are being considered.
Abstract: We consider the kinetic Ising models (Glauber dynamics) corresponding to the infinite volume Ising model in dimension 2 with nearest neighbor ferromagnetic interaction and under a positive external magnetic field h. Minimal conditions on the flip rates are assumed, so that all the common choices are being considered. We study the relaxation towards equilibrium when the system is at an arbitrary subcritical temperature T and the evolution is started from a distribution which is stochastically lower than the (−)-phase. We show that as h↘ 0 the relaxation time blows up as exp(λc(T)/h), with lgr;c(T) =w(T)2/(12 T m*(T)). Here m*(T) is the spontaneous magnetization and w(T) is the integrated surface tension of the Wulff body of unit volume. Moreover, for 0 < λ < λc, the state of the process at time exp(λ/h) is shown to be close, when h is small, to the (−)-phase. The difference between this state and the (−)-phase can be described in terms of an asymptotic expansion in powers of the external field. This expansion can be interpreted as describing a set of ?∞ continuations in h of the family of Gibbs distributions with the negative magnetic fields into the region of positive fields.
TL;DR: In this paper, the effect of a positive single ion anisotropy on the compensation temperature in a pure system with D only on spin-5/2 atoms is investigated, in order to clarify the characteristic feature of the temperature dependence of the total magnetization M observed in a molecular-based magnetic material.
Abstract: The magnetic properties of a diluted spin-2 and spin-5/2 ferrimagnetic Ising system are investigated on the basis of the effective-field theory with correlations. In particular, the effect of a positive single-ion anisotropy D on the compensation temperature in a pure system with D only on spin-5/2 atoms is investigated, in order to clarify the characteristic feature of the temperature dependence of the total magnetization M observed in a molecular-based magnetic material, . The influences of D and the concentrations of magnetic atoms on the properties of the system on a honeycomb lattice are examined. The results show that several (two or three) compensation points are possible in the diluted system with special values of D and concentrations of magnetic atoms.
TL;DR: In this article, the quantum phase transition in the two-dimensional random Ising model in a transverse field was studied by Monte Carlo simulations and the results were similar to those known analytically in one dimension.
Abstract: We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one dimension. At the critical point the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single continuously varying exponent, ${z}^{\ensuremath{'}}$, which diverges at the critical point, as in one dimension. Consequently, the zero temperature susceptibility diverges for a range of parameters about the transition.
TL;DR: A simple model is proposed--the two-state Worm Like Chain--to describe the elasticity of the recently discovered stress-induced transformation from B-DNA to S-DNA, and it is used to show that conformational fluctuations of the chain play a role also for the B to S transformation.
TL;DR: In this article, a mean-field approach was used to study the kinetics of a classical mixed Ising ferrimagnetic model on a square lattice, in which the two interpenetrating square sublattices have spins.
Abstract: We present a study, within a mean-field approach, of the kinetics of a classical mixed Ising ferrimagnetic model on a square lattice, in which the two interpenetrating square sublattices have spins $\ensuremath{\sigma}=\ifmmode\pm\else\textpm\fi{}1/2$ and $S=\ifmmode\pm\else\textpm\fi{}1,0.$ The kinetics is described by a Glauber-type stochastic dynamics in the presence of a time-dependent oscillating external field and a crystal field interaction. We can identify two types of solutions: a symmetric one, where the total magnetization $M$ oscillates around zero, and an antisymmetric one where $M$ oscillates around a finite value different from zero. There are regions of the phase space where both solutions coexist. The dynamical transition from one regime to the other can be of first or second order depending on the region in the phase diagram. Depending on the value of the crystal field we found up to two dynamical tricritical points where the transition changes from continuous to discontinuous. Also, we perform a similar study on the Blume-Capel $(S=\ifmmode\pm\else\textpm\fi{}1,0)$ model and find strong differences between its behavior and the one of the mixed model.
TL;DR: In this paper, the authors introduce simulated tempering and its application to the random field Ising model, and illustrate parallel tempering, and discuss some crucial technical details such as thermalization and volume scaling.
Abstract: I discuss optimized data analysis and Monte Carlo methods. Reweighting methods are discussed through examples, such as Lee-Yang zeroes in the Ising model and the absence of deconfinement in QCD. Reweighted data analysis and multihistogramming are also discussed. I introduce simulated tempering, and, as an example, its application to the random field Ising model. I illustrate parallel tempering, and discuss some crucial technical details such as thermalization and volume scaling. I give a general perspective by discussing umbrella methods and the multicanonical approach.
TL;DR: In this paper, the degeneracy of energy states is obtained with a Markovian process analogous to that of Metropolis used currently in canonical simulations, and the obtained histograms are much broader than those of the canonical histogram technique studied by Ferrenberg and Swendsen.
Abstract: We propose a new Monte Carlo technique in which the degeneracy of energy states is obtained with a Markovian process analogous to that of Metropolis used currently in canonical simulations. The obtained histograms are much broader than those of the canonical histogram technique studied by Ferrenberg and Swendsen. Thus we can reliably reconstruct thermodynamic functions over a much larger temperature scale also away from the critical point. We show for the two-dimensional Ising model how our new method reproduces exact results more accurately and using less computer time than the conventional histogram method. We also show data in three dimensions for the Ising ferromagnet and the Edwards Anderson spin glass.
TL;DR: In this paper, Monte Carlo simulations of the full 3D Lennard-Jones fluid in the critical region are performed within the grand canonical ensemble in conjunction with hyperspherical boundary conditions in order to take account of the algebraic attractive part of the pair potential.
Abstract: Monte Carlo simulations of the full, i.e. nontruncated, 3d Lennard-Jones fluid in the critical region are reported. The simulations are performed within the grand canonical ensemble in conjunction with hyperspherical boundary conditions in order to take account of the algebraic attractive part of the pair potential. Using mixed-field finite size scaling analysis and with the assumption of Ising criticality the critical temperature is estimated to be T*=1.326±0.002 and the critical density ρ*=0.316±0.002. Precised estimates of the critical energy per unit volume, pressure, chemical potential, and mixed-field parameters are also reported. The values obtained for the renormalization exponents yτ and yh are compatible with the 3d Ising values within the error bars.
TL;DR: In this paper, the nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation (in two dimensions) and by solving the mean-field dynamical equation of motion for the average magnetization.
Abstract: The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation (in two dimensions) and by solving the mean-field dynamical equation of motion for the average magnetization. The temperature variations of hysteretic loss (loop area) and the dynamic correlation have been studied near the transition point. The transition point has been identified as the minimum-correlation point. The hysteretic loss becomes maximum above the transition point. An analytical formulation has been developed to analyze the simulation results. A general relationship among hysteresis loop area, dynamic order parameter, and dynamic correlation has also been developed.
TL;DR: In this article, the authors considered a dissipation field (square gradient) of a passive scalar advected by incompressible turbulence and showed that the PDF of the dissipation is a nonperturbative object with respect to the inverse Peclet number.
Abstract: Probability distribution of the gradients of turbulent fields is probably the most remarkable manifestation of the intermittency of developed turbulence and related strong non-Gaussianity. A typical plot of the logarithm of gradient’s probability density function (PDF) (which would be parabolic for Gaussian statistics) is concave rather than convex, with a strong central peak and slowly decaying tails. This is natural for an intermittent field since rare strong fluctuations are responsible for the tails, while large quiet regions are related to the central peak. In particular, such PDFs were observed for the dissipation field (square gradient) of passive scalar advected by incompressible turbulence which is the subject of the present paper. We consider scalar advection within the framework of the Kraichnan model assuming velocity field to be delta correlated in time [1]. Most of the rigorous results on turbulent mixing have been obtained so far with the help of that model which is likely to play in turbulence the role the Ising model played in critical phenomena. High-order moments of the scalar were treated hitherto by the perturbation theory around Gaussian limits. Clearly, the kind of strongly nonGaussian PDF observed for gradients cannot be treated by any perturbation theory that starts from a Gaussian statistics as zero approximation. Since we consider developed turbulence with large Peclet number Pe (measuring relative strength of advection with respect to diffusion at the pumping scale), it is tempting to use Pe 21 as a small parameter. Yet any attempt to treat diffusion term perturbatively is doomed to fail because the PDF of the dissipation is a nonperturbative object with respect to the inverse Peclet number: it is zero at efi 0and zero diffusivity yet has nonzero limits
TL;DR: In this paper, the authors investigated the thermally activated magnetization switching of small ferromagnetic particles driven by an external magnetic field and found that the crossover from coherent rotation to nucleation is influenced by the size of the particle, the strength of the driving magnetic field, and the anisotropy.
Abstract: We investigate the thermally activated magnetization switching of small ferromagnetic particles driven by an external magnetic field. For low uniaxial anisotropy the spins can be expected to rotate coherently, while for sufficient large anisotropy they should behave Ising-like, i.e., the switching should then be due to nucleation. We study this crossover from coherent rotation to nucleation for a classical three-dimensional Heisenberg model with finite anisotropy. The crossover is influenced by the size of the particle, the strength of the driving magnetic field, and the anisotropy. We discuss the relevant energy barriers which have to be overcome during the switching, and find theoretical arguments which yield the energetically favorable reversal mechanisms for given values of the quantities above. The results are confirmed by Monte Carlo simulations of Heisenberg and Ising models.
TL;DR: In this paper, the effects of different single-ion anisotropies on the magnetic properties (phase diagram, total and sublattice magnetizations) of a mixed spin-1 and spin-3 2 Ising ferrimagnetic system on a honeycomb lattice were investigated.
Abstract: Within an effective-field formalism we study effects of different single-ion anisotropies on the magnetic properties (phase diagram, total and sublattice magnetizations) of a mixed spin-1 and spin- 3 2 Ising ferrimagnetic system on a honeycomb lattice. At a finite temperature we obtain quite a rich phase diagram with tricritical and fourth-order points. Some outstanding features are found in the temperature dependences of total and sublattice magnetizations.
TL;DR: In this article, the authors investigated successive magnetic phase transitions in a frustrated triangular lattice antiferromagnet (TLA) with single crystals and found that the magnetic structure of the intermediate-temperature phase between T N 1 and T N 2 is a quasi-long range ordered sinusoidally amplitude-modulated structure with a temperature dependent propagation wave vector.
Abstract: We reinvestigated successive magnetic phase transitions ( T N1 ∼14.0 K, T N2 ∼10.5 K) in a frustrated triangular lattice antiferromagnet (TLA) CuFeO 2 by neutron diffraction measurements using single crystals. The magnetic structure of the intermediate-temperature phase between T N1 and T N2 is found to be a quasi -long range ordered sinusoidally amplitude-modulated structure with a temperature dependent propagation wave vector ( q q 0). These features of successive phase transitions are well explained by reinvestigated Monte-Carlo simulation of a 2D Ising TLA with competing exchange interactions up to 3rd neighbors, in spite of the Heisenberg spin character of orbital singlet Fe 3+ magnetic ions.
TL;DR: In this article, a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field was studied using Monte Carlo simulations and analytical theory.
Abstract: We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below T{sub c}. For these restricted parameters, the magnetization switches through random nucleation of a {ital single} droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for themore » interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise. {copyright} {ital 1998} {ital The American Physical Society}« less
TL;DR: In this article, the crossover of the susceptibility critical exponent γ from its Ising value γ = 1.24 to the mean-field value of γ=1 is sharp and nonmonotonic.
Abstract: The near-critical behavior of the susceptibility deduced from light-scattering measurements in a ternary liquid mixture of 3-methylpyridine, water, and sodium bromide has been determined. The measurements have been performed in the one-phase region near the lower consolute points of samples with different concentrations of sodium bromide. A crossover from Ising asymptotic behavior to mean-field behavior has been observed. As the concentration of sodium bromide increases, the crossover becomes more pronounced, and the crossover temperature shifts closer to the critical temperature. The data are well described by a model that contains two independent crossover parameters. The crossover of the susceptibility critical exponent γ from its Ising value γ=1.24 to the mean-field value γ=1 is sharp and nonmonotonic. We conclude that there exists an additional length scale in the system due to the presence of the electrolyte which competes with the correlation length of the concentration fluctuations. An analogy with crossover phenomena in polymer solutions and a possible connection with multicritical phenomena is discussed.
TL;DR: A cooperative model is presented, in which coupling between neighboring receptor dimers enhances the sensitivity with which stimuli can be detected, without diminishing the range of chemoeffector concentration over which chemotaxis can operate.
Abstract: Bacterial chemotaxis is controlled by the signaling of a cluster of receptors. A cooperative model is presented, in which coupling between neighboring receptor dimers enhances the sensitivity with which stimuli can be detected, without diminishing the range of chemoeffector concentration over which chemotaxis can operate. Individual receptor dimers have two stable conformational states: one active, one inactive. Noise gives rise to a distribution between these states, with the probability influenced by ligand binding, and also by the conformational states of adjacent receptor dimers. The two-state model is solved, based on an equivalence with the Ising model in a randomly distributed magnetic field. The model has only two effective parameters, and unifies a number of experimental findings. According to the value of the parameter comparing coupling and noise, the signal can be arbitrarily sensitive to changes in the fraction of receptor dimers to which the ligand is bound. The counteracting effect of a change of methylation level is mapped to an induced field in the Ising model. By returning the activity to the prestimulus level, this adapts the receptor cluster to a new ambient concentration of chemoeffector, and ensures that a sensitive response can be maintained over a wide range of concentrations.
TL;DR: In this article, a novel method for numerical spin glass investigations is introduced: Simulations of two replica at fixed temperature, weighted to achieve a broad distribution of the Parisi overlap parameter q (multioverlap), which makes it possible to obtain reliable results about spin glass tunneling barriers.
Abstract: We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted to achieve a broad distribution of the Parisi overlap parameter q (multioverlap). We demonstrate the feasibility of the approach by studying the 3D Edwards-Anderson Ising (J{sub ik}={plus_minus}1) spin glass in the broken phase ({beta}=1). This makes it possible to obtain reliable results about spin glass tunneling barriers. In addition, our results indicate a nontrivial scaling behavior of the canonical q distributions not only at the freezing point but also deep in the broken phase. {copyright} {ital 1998} {ital The American Physical Society}
TL;DR: In this article, the Heisenberg model on a 2-chain spin-1/2 ladder with second neighbor interactions is studied by using series expansions about the Ising and dimer limits, numerical diagonalization, and by Abelian bosonization analysis.
Abstract: The Heisenberg model on a 2-chain spin-1/2 ladder with frustrating second neighbor interactions is studied by using series expansions about the Ising and dimer limits, numerical diagonalization, and by Abelian bosonization analysis. The phase diagram is determined, and pair correlations and the complete dispersion relations for the triplet spin-wave excitations are also computed.