High Precision Renormalization Group Study of the Roughening Transition

TL;DR

This study confirms the Kosterlitz-Thouless nature of the roughening transition in three solid-on-solid models using renormalization group matching and high-precision Monte Carlo simulations, providing accurate critical parameters.

Contribution

It introduces a high-precision renormalization group matching method to analyze the roughening transition across multiple models, enhancing the accuracy of critical point estimates.

Findings

Critical coupling for XY model: 1.1197(5)

Roughening coupling for Discrete Gaussian: 0.6645(6)

Roughening coupling for ASOS model: 0.8061(3)

Abstract

We confirm the Kosterlitz-Thouless scenario of the roughening transition for three different Solid-On-Solid models: the Discrete Gaussian model, the Absolute-Value-Solid-On-Solid model and the dual transform of the XY model with standard (cosine) action. The method is based on a matching of the renormalization group flow of the candidate models with the flow of a bona fide KT model, the exactly solvable BCSOS model. The Monte Carlo simulations are performed using efficient cluster algorithms. We obtain high precision estimates for the critical couplings and other non-universal quantities. For the XY model with cosine action our critical coupling estimate is $\beta_R^{XY}=1.1197(5)$. For the roughening coupling of the Discrete Gaussian and the Absolute-Value-Solid-On-Solid model we find $K_R^{DG}=0.6645(6)$ and $K_R^{ASOS}=0.8061(3)$, respectively.