Magnetic exponent for the long-range bond disordered Potts model

TL;DR

This paper investigates the critical magnetic behavior of two-dimensional long-range disordered Potts models using conformal field theory and Monte Carlo simulations, revealing a crossover between universality classes.

Contribution

It extends the renormalization group analysis to the magnetic sector of long-range disordered Potts models and compares predictions with numerical simulations.

Findings

Computed leading corrections to the spin scaling dimension.

Provided numerical evidence of a crossover between long-range and short-range universality classes.

Included the long-range disorder Ising model as a special case.

Abstract

We consider the critical behavior of two-dimensional Potts models in presence of a bond disorder in which the correlation decays as a power law. In some recent work the thermal sector of this theory was investigated by a renormalization group computation based on perturbed conformal field theory. Here we apply the same approach to study instead the magnetic sector. In particular we compute the leading corrections to the Potts spin scaling dimension. Our results include as a special case the long-range disorder Ising model. We compare our prediction to Monte-Carlo simulations. Finally, by studying the magnetization scaling function, we show a clear numerical evidence of a cross-over between the long-range and the short-range class of universality.