Progress of Theoretical Physics

Two-Dimensional Ising Models with Layered Quenched Bond Randomness. I: --The Devil's Staircase of the Distribution Function and the Specific Heat for Random Ferromagnets--

Y. Akutsu, K. Matsumoto

Published Jun 1, 1986• 2 citations

Abstract

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.

DOI: 10.1143/ptp.75.1304

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