Low Temperature Properties of the Random Field Potts Chain

TL;DR

This paper studies the low temperature behavior of the random field Potts model using exact groundstate calculations and transfer matrix methods, revealing domain structures and scaling behaviors similar to the Ising case across various q.

Contribution

It provides a detailed analysis of the domain structure, size distribution, and response properties of the q-state random field Potts model, extending understanding beyond the Ising case.

Findings

Domain structure and Zeeman energy resemble the q=2 case for general q.

Domain size distribution is exponential and scales similarly for all q.

Chaos exponent is found to be 1 for q=2,...,5.

Abstract

The random field q-States Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found that the domain structure and the Zeeman energy of the domains resembles for general q the random field Ising case (q=2), which is also the expectation based on a random-walk picture of the groundstate. The domain size distribution is exponential, and the scaling of the average domain size with the disorder strength is similar for q arbitrary. The zero-temperature properties are compared to the equilibrium spin states at small temperatures, to investigate the effect of local random field fluctuations that imply locally degenerate regions. The response to field pertubabtions ('chaos') and the susceptibility are investigated. In particular for the chaos exponent it is found to be 1 for q = 2,...,5. Finally for q=2 (Ising case) the domain length distribution is studied for correlated random fields.