Crossover between a Short-range and a Long-range Ising model

Abstract

Recently, it has been found that an effective long-range interaction is realized among local bistable variables (spins) in systems where the elastic interaction causes ordering of the spins. In such systems, generally we expect both long-range and short-range interactions to exist. In the short-range Ising model, the correlation length diverges at the critical point. In contrast, in the long-range interacting model the spin configuration is always uniform and the correlation length is zero. As long as a system has non-zero long-range interactions, it shows criticality in the mean-field universality class, and the spin configuration is uniform beyond a certain scale. Here we study the crossover from the pure short-range interacting model to the long-range interacting model. We investigate the infinite-range model (Husimi-Temperley model) as a prototype of this competition, and we study how the critical temperature changes as a function of the strength of the long-range interaction. This model can also be interpreted as an approximation for the Ising model on a small-world network. We derive a formula for the critical temperature as a function of the strength of the long-range interaction. We also propose a scaling form for the spin correlation length at the critical point, which is finite as long as the long-range interaction is included, though it diverges in the limit of the pure short-range model. These properties are confirmed by extensive Monte Carlo simulations.

References in corpus (5)

• Simple Two-Dimensional Model for the Elastic Origin of Cooperativity among Spin States of Spin-Crossover Complexes
• Realization of the mean-field universality class in spin-crossover materials
• Monte Carlo simulation of pressure-induced phase transitions in spin-crossover materials
• Critical Binder cumulant in two-dimensional anisotropic Ising models
• Structure of Metastable States in Phase Transitions with High-Spin Low-Spin Degree of Freedom

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• Monte Carlo Simulations of the Critical Properties of a Ziff-Gulari-Barshad model of Catalytic CO Oxidation with Long-range Reactivity
• Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions
• Cooperative Phenomena in Spin Crossover Systems
• Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams
• The Origin of Mean-Field Behavior in an Elastic Ising Model
• Phase diagrams and free-energy landscapes for model spin-crossover materials with antiferromagnetic-like nearest-neighbor and ferromagnetic-like long-range interactions
• Monte Carlo Studies of the Ising Antiferromagnet with a Ferromagnetic Mean-field Term
• Spin-state smectics in spin crossover materials
• Mean-field models with short-range correlations
• Adatom pair distribution up to half coverage: O-Pd(100)
• Fluctuations and universality in a catalysis model with long-range reactivity
• Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions
• Crossover in the Ordered Phase in the Non-Mermin-Wagner-Hohenberg Regime of Spin Models with Long-Range Coupling