The square-lattice F model revisited: a loop-cluster update scaling study

TL;DR

This paper revisits the square-lattice F model, an exactly solvable system with a Kosterlitz-Thouless phase transition, using advanced Monte Carlo methods to better understand its critical properties and scaling behavior.

Contribution

It introduces a loop-cluster update Monte Carlo approach to analyze the F model, focusing on critical properties not exactly known and refining finite-size scaling techniques.

Findings

Accurate determination of polarizability in the critical phase

Scaling dimensions consistent with exact solutions

Identification of correction terms in finite-size scaling

Abstract

The six-vertex F model on the square lattice constitutes the unique example of an exactly solved model exhibiting an infinite-order phase transition of the Kosterlitz-Thouless type. As one of the few non-trivial exactly solved models, it provides a welcome gauge for new numerical simulation methods and scaling techniques. In view of the notorious problems of clearly resolving the Kosterlitz-Thouless scenario in the two-dimensional XY model numerically, the F model in particular constitutes an instructive reference case for the simulational description of this type of phase transition. We present a loop-cluster update Monte Carlo study of the square-lattice F model, with a focus on the properties not exactly known such as the polarizability or the scaling dimensions in the critical phase. For the analysis of the simulation data, finite-size scaling is explicitly derived from the exact solution and plausible assumptions. Guided by the available exact results, the careful inclusion of correction terms in the scaling formulae allows for a reliable determination of the asymptotic behaviour.