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Physica A Statistical Mechanics and its Applications

The three-dimensional dilute Ising magnet

Jian‐Sheng Wang, M. Wöhlert, Heinz Mühlenbein, Debashish Chowdhury

Published Jul 1, 1990• 38 citations
Publisher
DOI
10.1016/0378-4371(90)90010-p

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We study the crossover behaviors that can be observed in the high-temperature phase of three-dimensional dilute spin systems, using a field-theoretical approach. In particular, for randomly dilute Ising systems we consider the Gaussian-to-random and the pure-Ising-to-random crossover, determining the corresponding crossover functions for the magnetic susceptibility and the correlation length. Moreover, for the physically interesting cases of dilute Ising, XY, and Heisenberg systems, we estimate several universal ratios of scaling-correction amplitudes entering the high-temperature Wegner expansion of the magnetic susceptibility, of the correlation length, and of the zero-momentum quartic couplings.
Self-averaging of singular thermodynamic quantities at criticality for randomly and thermally diluted three-dimensional Ising systems has been studied by the Monte Carlo approach. Substantially improved self-averaging is obtained for critically clustered (critically thermally diluted) vacancy distributions in comparison with the observed self-averaging for purely random diluted distributions. Critically thermal dilution, leading to maximum relative self-averaging, corresponds to the case when the characteristic vacancy ordering temperature (theta) is made equal to the magnetic critical temperature for the pure three-dimensional (3D) Ising systems (T(3D)(c)). For the case of a high ordering temperature (theta>>T(3D)(c)), the self-averaging obtained is comparable to that in a randomly diluted system.