Logarithmic corrections in the two-dimensional Ising model in a random surface field

TL;DR

This study investigates how weak random surface fields affect the critical behavior of the 2D Ising model, confirming logarithmic corrections predicted by field theory through extensive Monte Carlo simulations.

Contribution

It provides numerical evidence supporting the field-theoretical prediction of logarithmic corrections due to marginally irrelevant surface disorder in the 2D Ising model.

Findings

Effective critical exponents show logarithmic dependence on temperature and size.

Results align with theoretical predictions of marginally irrelevant perturbations.

Monte Carlo data confirms the presence of logarithmic corrections in critical behavior.

Abstract

In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The calculated effective (temperature or size dependent) critical exponents fit with the field-theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system's critical behaviour.