Critical Behaviour of Random Bond Potts Models: A Transfer Matrix Study

TL;DR

This study investigates how quenched random-bond impurities affect the phase transitions in the two-dimensional Potts model, revealing continuous variation of critical exponents and unifying different universality classes.

Contribution

It provides a transfer matrix analysis combined with conformal invariance to characterize the universality classes of the disordered Potts model for q>4.

Findings

First-order transitions are softened by impurities for q>4.

Magnetic exponent beta/nu varies continuously with q.

Correlation length exponent nu is approximately 1.

Abstract

We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q>4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting universality classes by combining transfer matrix data with conformal invariance. The magnetic exponent beta/nu varies continuously with q, assuming non-Ising values for q>4, whereas the correlation length exponent nu is numerically consistent with unity. We present evidence for the correctness of a formerly proposed phase diagram, unifying pure, percolative and non-trivial random behaviour.