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Progress of Theoretical Physics

Monte Carlo Simulation for Random Mixtures of a Three-Dimensional Ising Site Model. II

T. Tatsumi

Published May 1, 1978• 12 citations
Publisher

Abstract

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.

DOI
10.1143/ptp.59.1437

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Journal of the Physical Society of Japan•Jan 15, 1997•3 citations
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.
We study a short-range site-random Ising model in three dimensions (3D) using a Monte Carlo (MC) method and find a phase transition to a spin glass (SG) phase at a very high temperature ( T c ≃2.83 J). Values of the critical exponents estimated from a finite-size scaling analysis are different from those in both the 3D∓J\mp J∓J Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.
First results of massive Monte Carlo simulations of the d=3 Ising spin-glass with \ifmmode\pm\else\textpm\fi{}J bond distribution, performed on a fast special purpose computer, are presented. A qualitative change in the behavior of the system and best fits for the spin-glass correlation length and relaxation time favor equilibrium phase transition at Tc{\mathrm{T}}_{\mathrm{c}}Tc​/J\ensuremath{\approxeq}1.2. .AE
The three-dimensional site-random Ising model consisting of two types of magnetic ions, A and B, is investigated by means of the exchange Monte Carlo method. The nearest-neighbor interactions are antiferromagnetic (AF) for the B-B pair and ferromagnetic (FM) otherwise. A uniform FM or AF ordering is found to exist in a wide range of concentration c of A ions, in contrast with the bond-random Ising model such as the ± J model. The phase diagram is found to be symmetric on the c – T plane, though the ratio of the FM bonds to AF ones is asymmetric with respect to c =1/2. Spin configurations of degenerate ground states and their cluster structure are also studied. Even in the system with c =0.55, there exists only a unique rigid cluster which includes about 90% of spins and that cluster shows nonvanishing uniform magnetization. These results strongly suggest that the present model has neither a spin glass phase nor an FM-AF mixed phase, though their existence in a quite narrow region around c =1/2 has not been completely excluded yet.