Low temperature properties of the random field Potts chain

Abstract

The random field q-States Potts model is investigated using exact groundstates and finitetemperature 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). This is also the expected outcome 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 perturbations ('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.