Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Modern Physics Letters B

Phase Diagram of the Semi-Infinite Ising Model in a Random Field

A.S. de Arruda, W. Figueiredo

Published Sep 20, 1997• 12 citations
Publisher

Abstract

We determine the phase diagram of the semi-infinite Ising model in a cubic lattice with a trimodal distribution of random fields on the surface. We use the mean-field renormalization group with the smallest possible clusters to show that a very small dilution of the random field at surface is sufficient to destroy the tricritical behavior.

DOI
10.1142/s0217984997001183

Related papers

Mean-field renormalization-group approaches to the surface on a semi-infinite Ising model with a random surface field

Gang Sun

We study the critical behavior of the surface on a semi-infinite simple-cubic-lattice Ising model with a bimodal random surface field by a large-cell mean-field renormalization-group method. Our results show that a surface ferromagnetic phase exists at weak random fields above the bulk critical temperature, and no signs of the tricritical point are found until the surface critical temperature decreases to that of the bulk.

Physical review. B, Condensed matter•Feb 1, 1995•1 citation

Field distributions and tricritical points in a random-field Ising model: Mean-field renormalization-group approach

A.S. de Arruda, W. Figueiredo, Rafael M. Sebastianes +1 more

The form of the field distribution, in a random-field Ising model, is known to play an important role in determining the order of the phase transition and the existence of a tricritical point. We have studied a random-field Ising model with a trimodal distribution (sum of three \ensuremath{\delta} functions), which simulates a Gaussian distribution for a certain range of its parameters, within the mean-field renormalization-group scheme. We have considered clusters of one, two, and four spins, and the recursion relations for the determination of the fixed points are numerically analyzed. Using this analysis we have constructed the phase diagram of the system in the space of coupling (K), field (h), and zero-field probability (p). It is shown that the line of tricritical points ends for values of p near (2/3, very different from that obtained in the usual mean-field approximation. Mean-field renormalization-group (p\ensuremath{\simeq}(2/3) results are found to be consistent with the equivalence of the trimodal and Gaussian (absence of tricritical points) distributions until the fourth-order moments for p=(2/3.

Physical review. B, Condensed matter•Mar 1, 1989•24 citations

Mean-field theory of the semi-infinite spin-1/2 Ising model with random surface and bulk fields

M. Saber

All the possible phase diagrams of a three-dimensional semi-infinite spin-1/2 Ising model in a random field as a function of the ratio of bulk and surface interactions and the ratio of bulk and surface fields have been determined. Within the framework of the mean-field approximation eight generic types of phase diagrams can be found. It is also shown that such a system can exhibit a variety of phase transitions and multi-critical points.

Journal of Physics C Solid State Physics•Jun 30, 1987•24 citations

CRITICAL BEHAVIOR AT THE SURFACE OF A SEMI INFINITE MIXED SPIN ISING SYSTEM WITH SURFACE RANDOM FIELD

GAO ZHAN, Zhenlin Wang, XU JIAN-HONG +1 more

In this paper,a renormalization group scheme within the framework of the mean field theory is used to investigate the critical behavior at the surface of a semi infinite Ising system with mixed spins,i.e.S=1 at the surface and σ=1/2 in the bulk.The effects of a random field on the surface phase diagrams are obtained.

Acta Physica Sinica•Jan 1, 1997•1 citation

Numerical Calculations for the Surface on a Semi-Infinite Ising Model with a Random Surface Field

Gang Sun, Jie Yang

We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormalization group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large random field.

Communications in Theoretical Physics•Jan 30, 1995•1 citation

STUDY OF SURFACE MAGNETISM IN A SEMI-INFINITE ISING FERROMAGNETIC SYSTEM

JIANG QIN, Zhenya Li, 苏州大学物理系

We use the mean field renormalization group method to treat the semi-infinite Ising ferromagnetic system with the amorphization of the surface. The critical behavior of the surface with a surface random field, including critical temperature, the possibility of tricritical and reentrant phenomena, are investigated in detail.

Acta Physica Sinica•Jan 1, 1989•1 citation
We determine the phase diagram of the semi-infinite Ising model in a cubic lattice with a trimodal distribution of random fields on the surface. We use the mean-field renormalization group with the smallest possible clusters to show that a very small dilution of the random field at surface is sufficient to destroy the tricritical behavior.
The form of the field distribution, in a random-field Ising model, is known to play an important role in determining the order of the phase transition and the existence of a tricritical point. We have studied a random-field Ising model with a trimodal distribution (sum of three \ensuremath{\delta} functions), which simulates a Gaussian distribution for a certain range of its parameters, within the mean-field renormalization-group scheme. We have considered clusters of one, two, and four spins, and the recursion relations for the determination of the fixed points are numerically analyzed. Using this analysis we have constructed the phase diagram of the system in the space of coupling (K), field (h), and zero-field probability (p). It is shown that the line of tricritical points ends for values of p near (2/3, very different from that obtained in the usual mean-field approximation. Mean-field renormalization-group (p\ensuremath{\simeq}(2/3) results are found to be consistent with the equivalence of the trimodal and Gaussian (absence of tricritical points) distributions until the fourth-order moments for p=(2/3.
We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormalization group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large random field.