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Two-dimensional ising models with layered quenched bond randomness(2) : The boundary magnetization and its universal critical behavior

Kazuyuki Matsumoto, Yasuhiro Akutsu, 和幸 松元, Yasuhiro Akutsu

Published Mar 20, 1988• 0 citations
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Abstract

(Received ) This paper investigates the generalized McCoy-Wu type random Ising model. It is found that boundary magnetization behaves as (TciT) fl 0 , fl 0 = 1:0 just below the ’critical temperature’. From numerical analyses it is revealed that this type of critical behavior, fl 0 = 1:0, would be universal for any type of randomness. This universal behavior is explained in terms of the destruction of the devil’s staircase structure. As an observable result of this model, the integrated distribution function of boundary magnetization is suggested.

DOI
10.14983/00000329

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(Received ) This paper investigates the generalized McCoy-Wu type random Ising model. It is found that boundary magnetization behaves as (TciT) fl 0 , fl 0 = 1:0 just below the ’critical temperature’. From numerical analyses it is revealed that this type of critical behavior, fl 0 = 1:0, would be universal for any type of randomness. This universal behavior is explained in terms of the destruction of the devil’s staircase structure. As an observable result of this model, the integrated distribution function of boundary magnetization is suggested.
Exactly solvable two-dimensional Ising models with McCoy-Wu type layered quenched bond randomness are studied both analytically and numerically. For binary type bond distributions, it is proved that the distribution function of a random variable, which appears in the exact solution, shows the devil's staircase structure for a certain range of temperatures. By using a direct iternation method, the free energy and the specific heat are calculated in such a way as to give the numerically exact solution for a finite system. The specific heat does not show divergent behavior around the ‘critical’ temperature. The behavior is explained in terms of the distribution function.
We consider two-dimensional Ising models with randomly distributed ferromagnetic bonds and study the local critical behavior at defect lines by extensive Monte Carlo simulations. Both for ladder and chain type defects, non-universal critical behavior is observed: the critical exponent of the defect magnetization is found to be a continuous function of the strength of the defect coupling. Analyzing corresponding stability conditions, we obtain new evidence that the critical exponent ννν of the bulk correlation length of the random Ising model does not depend on dilution, i.e. ν=1ν=1ν=1.
We consider the two-dimensional randomly site diluted Ising model and the random-bond +/-J Ising model (also called the Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of thermodynamic quantities can be derived from a set of renormalization-group equations, in which disorder is a marginally irrelevant perturbation at the two-dimensional Ising fixed point. We discuss their solutions, focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder. Then, we present a finite-size scaling analysis of high-statistics Monte Carlo simulations. The numerical results confirm the renormalization-group predictions, and in particular the universality of the logarithmic corrections to the Ising behavior due to quenched dilution.