Phase Transitions of the Variety of Random-Field Potts Models

TL;DR

This paper investigates phase transitions in three-dimensional random-field q-state Potts models using renormalization-group theory, revealing how different types of randomness affect phase diagrams and the stability of ordered phases.

Contribution

It provides the first detailed renormalization-group analysis of various random-field types in 3D Potts models, extending understanding beyond the Ising case.

Findings

Ordered phase persists up to a random-field threshold in 3D.

Phase diagrams are similar across different types of randomness for a given q.

Low-q models have higher transition temperatures, high-q models withstand higher random fields.

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.