Phase Transitions of the Variety of Random-Field Potts Models

Abstract

The phase transitions of random-field q-state Potts models in d = 3 dimensions are studied by renormalization-group theory by exact solution of a hierarchical lattice and, equivalently, approximate Migdal-Kadanoff solutions of a cubic lattice. The recursion, under rescaling, of coupled random-field and random-bond (induced under rescaling by random fields) coupled probability distributions is followed to obtain phase diagrams. Unlike the Ising model (q = 2), several types of random fields can be defined for q >= 3 Potts models, including random-axis favored, random-axis disfavored, random-axis randomly favored or disfavored cases, all of which are studied. Quantitatively very similar phase diagrams are obtained, for a given q for the three types of field randomness, with the low-temperature ordered phase persisting, increasingly as temperature is lowered, up to random-field threshold in d = 3, which is calculated for all temperatures below the zero-field critical temperature. Phase diagrams thus obtained are compared as a function of q. The ordered phase in the low-q models reaches higher temperatures, while in the high-q models it reaches higher random fields. This renormalization-group calculation result is physically explained. (c) 2021 Elsevier B.V. All rights reserved.