Numerical Simulations of Random Phase Sine-Gordon Model and Renormalization Group Predictions

TL;DR

This paper demonstrates that finite size predictions derived from perturbative Renormalization Group theory align well with high-precision numerical simulations of the random phase sine-Gordon model near criticality, despite finite size effects.

Contribution

The study provides a finite size prediction based on RG arguments that accurately matches numerical simulations, clarifying the model's behavior near the critical point.

Findings

Finite size RG predictions agree with simulations for small coupling.

High-precision simulations confirm the RG-based finite size predictions.

Results improve understanding of finite size effects in the sine-Gordon model.

Abstract

Numerical Simulations of the random phase sine-Gordon model suffer from strong finite size effects preventing the non-Gaussian $\log^2 r$ component of the spatial correlator from following the universal infinite volume prediction. We show that a finite size prediction based on perturbative Renormalisation Group (RG) arguments agrees well with new high precision simulations for small coupling and close to the critical temperature.