# Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of $q$-state clock models

## TL;DR

This study investigates the Berezinskii-Kosterlitz-Thouless transition in $q$-state clock models of regular and Villain types with $q=5,6$, using large-scale Monte Carlo simulations to analyze phase transitions and universality.

## Contribution

It provides a comparative analysis of BKT transitions in regular and Villain clock models, highlighting the effectiveness of correlation ratio in identifying BKT phases.

## Key findings

- Both models exhibit double BKT transitions.
- Transition temperatures and exponents are estimated accurately.
- Transitions belong to the BKT universality class.

## Abstract

We study $q$-state clock models of regular and Villain types with $q=5,6$ using cluster-spin updates and observed double transitions in each model. We calculate the correlation ratio and size-dependent correlation length as quantities for characterizing the existence of Berezinskii-Kosterlitz-Thouless (BKT) phase and its transitions by large-scale Monte Carlo simulations. We discuss the advantage of correlation ratio in comparison to other commonly used quantities in probing BKT transition. Using finite size scaling of BKT type transition, we estimate transition temperatures and corresponding exponents. The comparison between the results from both types revealed that the existing transitions belong to BKT universality.