Phase-Transitions in Systems with Correlated Disorder
Physics and Astronomy
For random systems with quenched disorders distributed randomly in epsilon(R) dimensions and perfectly correlated in the remaining epsilon(C) dimensions, the renormalization-group theory has been performed in the past in two different ways. In the single-expansion method, one treats epsilon(C) as finite and expands the perturbation terms only for epsilon = d(c) - d, where d(c) is the upper critical dimension. In the double-expansion method, one treats epsilon(C) as infinitesimal and performs an additional expansion for epsilon(C). The former predicts smeared phase transitions, while the latter predicts sharp second-order phase transitions. We wish to find out which of the two predictions holds for a three-dimensional Ising model for which epsilon(C) = 2 and epsilon(R) = 1. We argue, using the replica method, that the spin correlation is isotropic for large distances as long as the fluctuation among the random bonds (in epsilon(R) dimensions) is sufficiently smaller than the thermal energy k(B)T. With parameters chosen to satisfy this condition in the model, a Monte Carlo simulation has been performed. The results favor a sharp second-order phase transition.
Physical Review B
(1992). Phase-Transitions in Systems with Correlated Disorder. Physical Review B, 45(5), 2217-2223.
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