# A numerical study of the F-model with domain-wall boundaries

## TL;DR

This study numerically investigates the F-model with domain-wall boundaries, confirming analytical predictions, analyzing phase transitions, and exploring local lattice properties, including oscillations and arctic curves, up to system size 512.

## Contribution

It provides a comprehensive numerical analysis of the F-model with domain-wall boundaries, validating analytical results and exploring phase transition behavior and local lattice structures.

## Key findings

- Numerical data agree with analytical arctic curves.
- Confirmed oscillations in vertex densities within the temperate region.
- Identified intricate oscillation patterns near frozen regions.

## Abstract

We perform a numerical study of the F-model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size as well as its asymptotics and leading finite-size corrections. To complement this picture we use a full lattice multi-cluster algorithm to study equilibrium properties of this model for systems of moderate size, up to L=512. We compare the energy to its exactly known large-L asymptotics. We investigate the model's infinite-order phase transition by means of finite-size scaling for an observable derived from the staggered polarization in order to test the method put forward in our recent joint work with Duine and Barkema. In addition we analyse local properties of the model. Our data are perfectly consistent with analytical expressions for the arctic curves. We investigate the structure inside the temperate region of the lattice, confirming the oscillations in vertex densities that were first observed by Sylju{\aa}sen and Zvonarev, and recently studied by Lyberg et al. We point out '(anti)ferroelectric' oscillations close to the corresponding frozen regions as well as 'higher-order' oscillations forming an intricate pattern with saddle-point-like features.