Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching

TL;DR

This paper accurately determines the critical couplings for roughening transitions in various lattice models using a renormalization group matching method with the BCSOS model, providing the most precise estimates to date.

Contribution

It introduces a renormalization group finite size scaling method matching interface observables with the exactly solvable BCSOS model to estimate roughening transition points.

Findings

Critical couplings for XY, Discrete Gaussian, and Absolute Value Solid-On-Solid models.

Most precise estimates for the roughening transition parameters.

Critical inverse temperature for the Ising interface.

Abstract

We study the roughening transition of the dual of the 2D XY model, of the Discrete Gaussian model, of the Absolute Value Solid-On-Solid model and of the interface in an Ising model on a 3D simple cubic lattice. The investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago. The basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable BCSOS model. Our estimates for the critical couplings are $\beta_R^{XY}=1.1199(1)$, $K_R^{DG}=0.6653(2)$ and $K_R^{ASOS}=0.80608(2)$ for the XY-model, the Discrete Gaussian model and the Absolute Value Solid-On-Solid model, respectively. For the inverse roughening temperature of the Ising interface we find $K_R^{Ising}= 0.40758(1)$. To the best of our knowledge, these are the most precise estimates for these parameters published so far.