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Coupled Ising models with disorder

Pascal Simon, Federico Ricci‐Tersenghi

Published Jan 1, 2000• 3 citations
OpenAlex

Abstract

In this paper we study the phase diagram of two Ising planes coupled by a standard spin-spin interaction with bond randomness in each plane. The whole phase diagram is analyzed by help of Monte Carlo simulations and field theory arguments. 1

Related papers

Coupled Ising models with disorder

Pascal Simon, Federico Ricci‐Tersenghi

In this paper we study the phase diagram of two Ising planes coupled by a standard spin-spin interaction with bond randomness in each plane. The whole phase diagram is analysed with the help of Monte Carlo simulations and field theory arguments.

arXiv:cond-mat/0008444•Journal of Physics A Mathematical and General•Aug 16, 2000•3 citations

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Spin-One Ising Model with Nearest-Neighbour and Next-Nearest-Neighbour Interactions

Motoyuki Tanaka, Takeshi Kawabe

Phase transitions of the spin-one Ising model with nearest-neighbour and next-nearest-neighbour interactions are investigated for a square lattice using a molecular-field theory and a Monte Carlo method. Special attention is paid to the effects of the biquadratic next-nearest-neighbour interaction on the phase transitions of the model. Phase diagrams characterizing types of phase transition are obtained for several values of the coupling constants. The existence of the multi-critical points and the successive phase transitions are also discussed in connection with these phase diagrams.

Journal of the Physical Society of Japan•Oct 1, 1983•10 citations
We examine the various kinds of phase diagrams that can occur in magnetic alloys when all the interactions have the same sign, i.e., all ferromagnetic. It is pointed out that these phase diagrams can be usefully cataloged in terms of the initial slope [$\frac{\ensuremath{\partial}(\mathrm{ln}{T}_{c})}{\ensuremath{\partial}p}$] of the transition temperature Tc{T}_{c}Tc​ with concentration ppp at the two points p=0p=0p=0 and p=1p=1p=1. For the two-dimensional Ising model, these initial slopes can be obtained exactly, using perturbation theory, for alloys involving either bond or site disorder. For site disorder we obtain results for a spin SSS in a host with spin \textonehalf{}. We show that mean-field theory is fairly reliable but fails to predict some kinds of phase diagrams that may occur.
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Cluster algorithms of Wolff and Glauber to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters
Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter, and the spin-spin correlation functions are studied in the nonequilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two-dimensional random field Ising model possesses long-range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long-range order in the system.
Phase transitions of the spin-one Ising model with nearest-neighbour and next-nearest-neighbour interactions are investigated for a square lattice using a molecular-field theory and a Monte Carlo method. Special attention is paid to the effects of the biquadratic next-nearest-neighbour interaction on the phase transitions of the model. Phase diagrams characterizing types of phase transition are obtained for several values of the coupling constants. The existence of the multi-critical points and the successive phase transitions are also discussed in connection with these phase diagrams.