Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond 8-state Potts Model

TL;DR

This study uses large-scale Monte Carlo simulations to analyze the critical behavior of the 8-state Potts model with random bonds, revealing that it does not belong to the 2D Ising universality class and providing specific critical exponents.

Contribution

The paper provides a detailed finite-size scaling analysis of the surface and bulk critical behavior in the random-bond 8-state Potts model, clarifying its universality class.

Findings

Model does not belong to the 2D Ising universality class.

Critical exponents differ from Ising values.

Finite-size scaling laws are satisfied.

Abstract

The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and deduce the corresponding critical exponents at the random fixed point using standard finite-size scaling techniques. The scaling laws are suitably satisfied. We find that a belonging of the model to the 2D Ising model universality class can be conclusively ruled out, and the dimensions of the relevant bulk and surface scaling fields are found to take the values $y_h=1.849$, $y_t=0.977$, $y_{h_s}=0.54$, to be compared to their Ising values: 15/8, 1, and 1/2.