Directed-loop Monte Carlo simulations of vertex models

TL;DR

This paper applies the directed-loop Monte Carlo algorithm to vertex models, specifically analyzing the six-vertex model with domain wall boundary conditions, revealing phase separation and boundary behavior.

Contribution

It demonstrates the use of the directed-loop Monte Carlo method for vertex models and explores phase boundaries and polarization behavior.

Findings

Identification of spatially separated ordered and disordered regions

Dependence of the boundary on model parameters

Predictions on polarization behavior in the thermodynamic limit

Abstract

We show how the directed-loop Monte Carlo algorithm can be applied to study vertex models. The algorithm is employed to calculate the arrow polarization in the six-vertex model with the domain wall boundary conditions (DWBC). The model exhibits spatially separated ordered and ``disordered'' regions. We show how the boundary between these regions depends on parameters of the model. We give some predictions on the behavior of the polarization in the thermodynamic limit and discuss the relation to the Arctic Circle theorem.