Tests of Conformal Invariance in Randomness Induced Second-Order Phase Transitions

TL;DR

This paper investigates whether conformal invariance holds in the two-dimensional 8-state Potts model with random bonds during second-order phase transitions, using transfer matrix and Monte Carlo methods to analyze correlation functions.

Contribution

It provides the first detailed numerical tests of conformal covariance in a disordered system undergoing a second-order phase transition.

Findings

Conformal transformations accurately describe correlation functions in the disordered system.

The order parameter scaling index matches previous independent measurements.

The energy density exponent is also determined with high precision.

Abstract

The conformal covariance of correlation functions is checked in the second-order transition induced by random bonds in the two-dimensional 8-state Potts model. The decay of correlations is obtained {\it via} transfer matrix calculations in a cylinder geometry, and large-scale Monte Carlo simulations give access to the correlations and the profiles inside a square with free or fixed boundary conditions, respectively. In both geometries, conformal transformations constrain the form of the spatial dependence, leading to accurate determinations of the order parameter scaling index in good agreement with previous independent determinations obtained through standard techniques. The energy density exponent is also computed.