Showing papers on "Ising model published in 1997"

Nonequilibrium Statistical Mechanics in One Dimension

Abstract: Part I. Reaction-Diffusion Systems and Models of Catalysis 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner 2. The coalescence process, A+A->A, and the method of interparticle distribution functions D. ben-Avraham 3. Critical phenomena at absorbing states R. Dickman Part II. Kinetic Ising Models 4. Kinetic ising models with competing dynamics: mappings, correlations, steady states, and phase transitions Z. Racz 5. Glauber dynamics of the ising model N. Ito 6. 1D Kinetic ising models at low temperatures - critical dynamics, domain growth, and freezing S. Cornell Part III. Ordering, Coagulation, Phase Separation 7. Phase-ordering dynamics in one dimension A. J. Bray 8. Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics V. Privman 9. Stochastic models of aggregation with injection H. Takayasu and M. Takayasu Part IV. Random Sequential Adsorption and Relaxation Processes 10. Random and cooperative sequential adsorption: exactly solvable problems on 1D lattices, continuum limits, and 2D extensions J. W. Evans 11. Lattice models of irreversible adsorption and diffusion P. Nielaba 12. Deposition-evaporation dynamics: jamming, conservation laws and dynamical diversity M. Barma Part V. Fluctuations In Particle and Surface Systems 13. Microscopic models of macroscopic shocks S. A. Janowsky and J. L. Lebowitz 14. The asymmetric exclusion model: exact results through a matrix approach B. Derrida and M. R. Evans 15. Nonequilibrium surface dynamics with volume conservation J. Krug 16. Directed walks models of polymers and wetting J. Yeomans Part VI. Diffusion and Transport In One Dimension 17. Some recent exact solutions of the Fokker-Planck equation H. L. Frisch 18. Random walks, resonance, and ratchets C. R. Doering and T. C. Elston 19. One-dimensional random walks in random environment K. Ziegler Part VII. Experimental Results 20. Diffusion-limited exciton kinetics in one-dimensional systems R. Kroon and R. Sprik 21. Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems R. Kopelman and A. L. Lin 22. Luminescence quenching as a probe of particle distribution S. H. Bossmann and L. S. Schulman Index.

Rational group decision making: A random field Ising model at T = 0

Abstract: A modified version of a finite random field Ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making. Fields may have a non-zero average. A postulate of minimum inter-individual conflicts is assumed. Interactions then produce a group polarization along one very choice which is however randomly selected. A small external social pressure is shown to have a drastic effect on the polarization. Individual bias related to personal backgrounds, cultural values and past experiences are introduced via quenched local competing fields. They are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones. In particular, compromise is found to results from the existence of individual competing bias. Conflict is shown to weaken group polarization. The model yields new psychosociological insights about consensus and compromise in groups.

Nonequilibrium phase transitions induced by multiplicative noise

Abstract: We review a mean-field analysis and give the details of a correlation function approach for spatially distributed systems subject to multiplicative noise, white in space and time. We confirm the existence of a pure noise-induced reentrant nonequilibrium phase transition in the model introduced in @C. Van den Broeck et al., Phys. Rev. Lett. 73, 3395 ~1994!#, give an intuitive explanation of its origin, and present extensive simulations in dimension d52. The observed critical properties are compatible with those of the Ising universality class. @S1063-651X~97!08704-7#

Generalized Dynamic Scaling for Critical Magnetic Systems

Abstract: The short-time behaviour of the critical dynamics for magnetic systems is investigated with Monte Carlo methods. Without losing the generality, we consider the relaxation process for the two dimensional Ising and Potts model starting from an initial state with very high temperature and arbitrary magnetization. We confirm the generalized scaling form and observe that the critical characteristic functions of the initial magnetization for the Ising and the Potts model are quite different.

Ising quantum chain is equivalent to a model of biological evolution

Abstract: One-dimensional systems, and quantum chains in particular, have long been important tools to understand, at least approximately, various physical situations, and there is even a recipe “how to reduce practically any problem to one dimension” [1]. As a complement, we present a problem of biochemical physics that may be mapped exactly onto a quantum chain. Selected examples can then be solved without approximation. In the theory of (molecular) biological evolution, various sequence space models are well established, the best known being Kauffman’s adaptive walk [2] and Eigen’s quasispecies model [3]. Whereas the former describes a hill-climbing process of a genetically homogeneous population in tunably rugged fitness landscapes, the latter includes the genetic structure of the population due to the balance between mutation and selection. For equal fitness landscapes, the quasispecies model is thus more difficult to treat than the corresponding adaptive walk. Some progress was made in [4] through the identification of the quasispecies model with a specific, anisotropic 2D Ising model: The mutation-selection matrix is equivalent to the row transfer matrix, with the mutation probability as a temperaturelike parameter, and error thresholds corresponding to phase transitions. This equivalence was exploited to treat simple fitness landscapes as well as spin-glass Hamiltonians with methods from statistical mechanics [5–7]. Of these results, most are approximate or numerical, and the few exact ones in [5] are of limited value as the order parameter was not calculated correctly. The quasispecies model assumes mutations to originate as replication errors on the occasion of reproduction events. An alternative was introduced in [8] and describes mutation and selection as going on in parallel; we would like to abbreviate it as para-muse (parallel mutation selection) model. In subsequent investigations [9,10], this model turned out to be both more powerful and structurally simpler than the quasispecies model. Which is the more appropriate one from the biological point of view amounts to the question

Magnetic anisotropy of Ca3Co2O6 with ferromagnetic Ising chains

Abstract: Magnetic properties of Ca 3 Co 2 O 6 with ferromagnetic Ising chains have been studied using oriented sample along the chain direction. From the extremely anisotropic behavior in its magnetization at low temperatures and in the temperature dependence of magnetic susceptibility, it is suggested that an octahedral Co 3+ is nonmagnetic, whereas a trigonal prismatic Co 3+ has a fictitious spin S '=1 with large single-ion anisotropy ( D ∼-25 K, g // ∼4). At low temperatures below 5 K, multisteps are observed in the magnetization, suggesting the existence of various magnetic structures. The pulsed magnetization measurements reveal that the response of ferromagnetic chains to the field is slow and varies as a function of temperature and Δ H /Δ t .

Classical critical behavior of spin models with long-range interactions

Abstract: We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for the exponents predicted by renormalization theory for systems in one, two, and three dimensions and accurately observe the predicted logarithmic corrections at the upper critical dimension. We give both theoretical and numerical evidence that above the upper critical dimension the decay of the critical spin-spin correlation function in finite systems consists of two different regimes. For one-dimensional systems our estimates for the critical couplings are more than two orders of magnitude more accurate than existing estimates. In two and three dimensions we are unaware of any other results for the critical couplings.

Topics in Disordered Systems

Abstract: 0 Introduction.- 1 Ground States of Disordered Ferromagnets.- 2 Ground States of Highly Disordered Systems.- 3 High Temperature States of Disordered Systems.- 4 Low Temperature States of Disordered Systems.- Appendix A: Infinite Geodesice and Measurability.- Appendix B: Disordered Systems and Metastates.

Description of periodic extreme gibbs measures of some lattice models on the Cayley tree

Abstract: The uniqueness of the translation-invariant extreme Gibbs measure for the antiferromagnetic Potts model with an external field and the existence of an uncountable number of extreme Gibbs measures for the Ising model with an external field on the Cayley tree are proved. The classes of normal subgroups of finite index of the Cayley tree group representation are constructed. The periodic extreme Gibbs measures, which are invariant with respect to subgroups of index 2, are constructed for the Ising model with zero external field. From these measures, the existence of an uncountable number of nonperiodic extreme Gibbs measures for the antiferromagnatic Ising model follows.

Triangular Antiferromagnets

Abstract: In this article we review the effects of magnetic frustation in the stacked triangular lattice. Frustration increases the degeneracy of the ground state, giving rise to different physics. In particular it leads to unique phase diagrams with multicritical points and novel critical phenomena. We describe the confrontation of theory and experiment for a number of systems with differing magnetic Hamiltonians; Heisenberg, Heisenberg with easy-axis anisotropy, Heisenberg with easy-plane anisotropy, Ising and singlet ground state. Interestingly each leads to different magnetic properties and phase diagrams. We also describe the effects of ferromagnetic, rather than antiferromagnetic, stacking and of small distortions of the triangular lattice.

Low temperature relaxational dynamics of the ising chain in a transverse field

Abstract: We present asymptotically exact results for the real time order parameter correlations of a class of $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ Ising models in a transverse field at low temperatures ( $T$) on both sides of the quantum critical point. The correlations are a product of a $T$-independent factor determined by quantum effects, and a $T$-dependent relaxation function which comes from a classical theory. We confirm our predictions by a no-free-parameter comparison with numerical studies on the nearest neighbor spin-1/2 model.

Numerical study of a mixed Ising ferrimagnetic system

Abstract: We present a study of a classical ferrimagnetic model on a square lattice in which the two interpenetrating square sublattices have spins one-half and one. This model is relevant for understanding bimetallic molecular ferrimagnets that are currently being synthesized by several experimental groups. We perform exact ground-state calculations for the model, and employ Monte Carlo and numerical transfer-matrix techniques to obtain the finite-temperature phase diagram for both the transition and compensation temperatures. When only nearest-neighbour interactions are included, our non-perturbative results indicate no compensation point or tricritical point at finite temperature, which contradicts earlier results obtained with mean-field analysis.

Delocalization transition via supersymmetry in one dimension

Abstract: We use supersymmetric (SUSY) methods to study the delocalization transition at zero energy in a one-dimensional tight-binding model of spinless fermions with particle-hole symmetric disorder. Like the McCoy-Wu random transverse-field Ising model to which it is related, the fermionic problem displays two different correlation lengths for typical and mean correlations. Using the SUSY technique, mean correlators are obtained as quantum-mechanical expectation values for a U(2$|$1,1) ``superspin.'' In the scaling limit, this quantum mechanics is closely related to a $0+1$-dimensional Liouville theory, allowing an interpretation of the results in terms of simple properties of the zero-energy wave functions. Our primary results are the exact two-parameter scaling functions for the mean single-particle Green's functions. We also show how the Liouville quantum-mechanics approach can be extended to obtain the full set of multifractal scaling exponents $\ensuremath{\tau}(q)$, $y(q)$ at criticality. A thorough understanding of the unusual features of the present theory may be useful in applying SUSY to other delocalization transitions.

Simulating ising spin glasses on a quantum computer

Abstract: A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum probability equal to the corresponding thermodynamic weight. The partition function is thus approximated efficiently. The algorithm neither suffers from critical slowing down nor gets stuck in local minima. The algorithm can be applied in any dimension, to a class of spin-glass Ising models with a finite portion of frustrated plaquettes, diluted Ising models, and models with a magnetic field.

Low-temperature properties of quantum antiferromagnetic chains with alternating spins and

Abstract: We study the low-temperature properties of S = 1 and S = 1/2 alternating spin chains with antiferromagnetic nearest-neighbour exchange couplings using analytical techniques as well as a quantum Monte Carlo method. The spin-wave approach predicts two different low-lying excitations, which are gapped and gapless, respectively. The structure of low-lying levels is also discussed using perturbation theory in terms of the strength of the Ising anisotropy. These analytical findings are compared with the results of quantum Monte Carlo calculations, and it turns out that spin-wave theory describes the present system well. We conclude that the quantum ferrimagnetic chain exhibits both ferromagnetic and antiferromagnetic aspects.

Bromide adsorption on ag(001): a potential induced two-dimensional ising order-disorder transition

Abstract: The adsorption of bromide on an Ag(001) electrode has been investigated using {ital in situ} x-ray scattering methods. With increasing potential, the bromide undergoes a second order phase transition from a lattice gas to an ordered c(2{times}2) structure. The order parameter is consistent with the 2D Ising model prediction {beta}=1/8 . A comparison of x-ray and electrochemical measurements indicates significant lateral disorder at low coverages which decreases with increasing coverage. {copyright} {ital 1997} {ital The American Physical Society}

Surface-directed spinodal decomposition: modelling and numerical simulations

Abstract: We critically review the modelling and simulations of surface-directed spinodal decomposition, namely, the dynamics of phase separation of a critical or near-critical binary mixture in the presence of a surface with a preferential attraction for one of the components of the mixture.

Zero-temperature hysteresis in the random-field Ising model on a Bethe lattice

Abstract: We consider the single-spin-flip dynamics of the random-field Ising model on a Bethe lattice at zero temperature in the presence of a uniform external field. We determine the average magnetization as the external field is varied from to by setting up the self-consistent field equations, which we show are exact in this case. The qualitative behaviour of magnetization as a function of the external field unexpectedly depends on the coordination number z of the Bethe lattice. For z = 3, with a Gaussian distribution of the quenched random fields, we find no jump in magnetization for any non-zero strength of disorder. For , for weak disorder the magnetization shows a jump discontinuity as a function of the external uniform field, which disappears for a larger variance of the quenched field. We determine exactly the critical point separating smooth hysteresis curves from those with a jump. We have checked our results by Monte Carlo simulations of the model on three- and four-coordinated random graphs, which for large system sizes give the same results as on the Bethe lattice, but avoid surface effects altogether.

Computing the roughening transition of Ising and solid-on-solid models by BCSOS model matching

Abstract: We study the roughening transition of the dual of the two-dimensional (2D) XY model, of the discrete Gaussian model, of the absolute value solid-on-solid model and of the interface in an Ising model on a three-dimensional (3D) simple cubic lattice. The investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago. The basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable body-centred solid-on-solid (BCSOS) model. Our estimates for the critical couplings are , and for the XY model, the discrete Gaussian model and the absolute value solid-on-solid model, respectively. For the inverse roughening temperature of the Ising interface we find . To the best of our knowledge, these are the most precise estimates for these parameters published so far.

Theory of the Random Field Ising Model

Abstract: A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in $d\le 2$ space dimensions for uncorrelated random fields, we consider different random field correlations and in particular the generation of uncorrelated from anti-correlated random fields by thermal fluctuations. In discussing the phase transition, we consider the transition to be characterized by a divergent correlation length and compare the critical exponents obtained from various methods (real space RNG, Monte Carlo calculations, weighted mean field theory etc.). The ferromagnetic transition is believed to be preceded by a spin glass transition which manifests itself by replica symmetry breaking. In the discussion of dynamical properties, we concentrate mainly on the zero temperature depinning transition of a domain wall, which represents a critical point far from equilibrium with new scaling relations and critical exponents.

Theory of the Random Field Ising Model

Abstract: A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in $d\le 2$ space dimensions for uncorrelated random fields, we consider different random field correlations and in particular the generation of uncorrelated from anti-correlated random fields by thermal fluctuations. In discussing the phase transition, we consider the transition to be characterized by a divergent correlation length and compare the critical exponents obtained from various methods (real space RNG, Monte Carlo calculations, weighted mean field theory etc.). The ferromagnetic transition is believed to be preceded by a spin glass transition which manifests itself by replica symmetry breaking. In the discussion of dynamical properties, we concentrate mainly on the zero temperature depinning transition of a domain wall, which represents a critical point far from equilibrium with new scaling relations and critical exponents.

A Monte Carlo finite size scaling study of charged hard-sphere criticality

Abstract: Monte Carlo simulations of the critical region of the restricted primitive model are reported. Using mixed-field finite size scaling analysis we show that the critical behavior is compatible with Ising like behavior although due to statistical error on the simulation data and large correction-to-scaling contributions mean-field behavior cannot be totally excluded. With the assumption of Ising criticality the critical temperature is estimated to be 0.0488±0.0002 and the critical density 0.080±0.005.

Real-space renormalization-group study of the two-dimensional Blume-Capel model with a random crystal field

Abstract: The phase diagram of the two-dimensional Blume-Capel model with a random crystal field is investigated within the framework of a real-space renormalization-group approximation. Our results suggest that, for any amount of randomness, the model exhibits a line of Ising-like continuous transitions, as in the pure model, but no first-order transition. At zero temperature the transition is also continuous, but not in the same universality class as the Ising model. In this limit, the attractor (in the renormalization-group sense) is the percolation fixed point of the site diluted spin-1/2 Ising model. The results we found are in qualitative agreement with general predictions made by Berker and Hui on the critical behavior of random models.

Lectures on Probability Theory and Statistics: Ecole d'Ete de Probabilites de Saint-Flour XXVI - 1996

Abstract: Part I, Bertoin, J.: Subordinators: Examples and Applications: Foreword.- Elements on subordinators.- Regenerative property.- Asymptotic behaviour of last passage times.- Rates of growth of local time.- Geometric properties of regenerative sets.- Burgers equation with Brownian initial velocity.- Random covering.- Levy processes.- Occupation times of a linear Brownian motion.- Part II, Martinelli, F.: Lectures on Glauber Dynamics for Discrete Spin Models: Introduction.- Gibbs Measures of Lattice Spin Models.- The Glauber Dynamics.- One Phase Region.- Boundary Phase Transitions.- Phase Coexistence.- Glauber Dynamics for the Dilute Ising Model.- Part III, Peres, Yu.: Probability on Trees: An Introductory Climb: Preface.- Basic Definitions and a Few Highlights.- Galton-Watson Trees.- General percolation on a connected graph.- The first-Moment method.- Quasi-independent Percolation.- The second Moment Method.- Electrical Networks.- Infinite Networks.- The Method of Random Paths.- Transience of Percolation Clusters.- Subperiodic Trees.- The Random Walks RW (lambda) .- Capacity.-.Intersection-Equivalence.- Reconstruction for the Ising Model on a Tree,- Unpredictable Paths in Z and EIT in Z3.- Tree-Indexed Processes.- Recurrence for Tree-Indexed Markov Chains.- Dynamical Pecsolation.- Stochastic Domination Between Trees.

Large deviations and continuum limit in the 2D Ising model

Abstract: We study the 2D Ising model in a rectangular box ⁄L of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization P t2⁄L ae(t) when L ! 1 for values of the parameters of the model corresponding to the phase coexistence region, where the order parameter m ⁄ is strictly positive. We study in particular boundary eects due to an arbitrary real- valued boundary magnetic field. Using the self-duality of the model a large part of the analysis consists in deriving properties of the covariance function hae(0)ae(t)i, as |t| ! 1, at dual values of the parameters of the model. To do this analysis we establish new results about the high-temperature representation of the model. These results are valid for dimensions D ‚ 2 and up to the critical temperature. They give a complete non-perturbative exposition of the high-temperature representation. We then study the Gibbs measure conditioned by {| P t2⁄L ae(t)im|⁄L|| • |⁄L|L ic }, with 0 < c < 1/4 and im ⁄ < m < m ⁄ . We construct the continuum limit of the model and describe the limit by the solutions of a variational problem of isoperi- metric type.