Monte Carlo studies of critical phase behaviors of compressible Ising models

D. P. Landau

Monte Carlo simulations have begun to illuminate the nature of phase transitions and universality classes for compressible Ising models. A comprehensive analysis of a Landau-Ginsburg Wilson hamiltonian for systems with elastic degrees of freedom predicts that there should be four cases with different behavior, depending upon symmetries and thermodynamic constraints. We shall describe the results of careful Monte Carlo simulations for a simple compressible Ising model that can be easily modified to correspond to each of the four cases.

D. P. Landau, B. Dünweg, Mohamed Laradji +4 more

Bikas K. Chakrabarti

Luigi Cannavacciuolo, David Paul Landau

Extensive Monte Carlo simulations in the semi-grand-canonical ensemble are used to study the critical behavior of a three-dimensional compressible Ising model with antiferromagnetic interactions under constant volume conditions. Elastic forces between spins are introduced by the Stillinger-Weber potential and energy parameters are chosen in such a way that antiparallel spin ordering is favored, analogous to the antiferromagnetic coupling in the rigid Ising Hamiltonian. All the quantities analyzed strongly indicate that the system remains in the universality class of the standard (rigid) three-dimensional Ising model, in contrast with theoretical predictions.

T. Tatsumi

The critical properties of random mixtures of a three-dimensional Ising model have been studied with the Monte Carlo simulation for case III (JAA = JAB = -JBB = 1). It has been found that this system has ferro, antiferro and para phases but not the spin glass phase. The phase boundary between ferro and antiferro phases could not be determined explicitly. It also has been found that the critical behavior of this system changes with concentration.

J. A. Plascak, W. Figueiredo