Phase transitions of the variety of random-field Potts models

Alpar Türkoğlu and A. Nihat Berker

Physica A: Statistical Mechanics and its Applications, 2021, vol. 583, issue C

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.

Keywords: Phase transitions; Potts models; Random fields; Renormalization-group theory; Hierarchical models; Exact solutions (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:583:y:2021:i:c:s0378437121006129

DOI: 10.1016/j.physa.2021.126339

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