Phase-Transitions in Systems with Correlated Disorder

Authors

J.C. Lee, University of Southern MississippiFollow
R.L. Gibbs, Louisiana Tech University

Document Type

Article

Publication Date

2-1-1992

Department

Physics and Astronomy

School

Mathematics and Natural Sciences

Abstract

For random systems with quenched disorders distributed randomly in ε_R dimensions and perfectly correlated in the remaining ε_c dimensions, the renormalization-group theory has been performed in the past in two different ways. In the single-expansion method, one treats ε_c as finite and expands the perturbation terms only for ε=d_c-d, where d_c is the upper critical dimension. In the double-expansion method, one treats ε_c as infinitesimal and performs an additional expansion for ε_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 ε_c=2 and ε_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 ε_R dimensions) is sufficiently smaller than the thermal energy k_BT. 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.

Publication Title

Physical Review B

Volume

45

Issue

5

First Page

2217

Last Page

2223

Recommended Citation

Lee, J., Gibbs, R. (1992). Phase-Transitions in Systems with Correlated Disorder. Physical Review B, 45(5), 2217-2223.
Available at: https://aquila.usm.edu/fac_pubs/6734