Phase-Transitions in Systems with Correlated Disorder
Physics and Astronomy
Mathematics and Natural Sciences
For random systems with quenched disorders distributed randomly in εR dimensions and perfectly correlated in the remaining εc dimensions, the renormalization-group theory has been performed in the past in two different ways. In the single-expansion method, one treats εc as finite and expands the perturbation terms only for ε=dc-d, where dc is the upper critical dimension. In the double-expansion method, one treats εc as infinitesimal and performs an additional expansion for εc. 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 εc=2 and εR=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 εR dimensions) is sufficiently smaller than the thermal energy kBT. 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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