Non-Kosterlitz-Thouless transitions for the $q$-state clock models

TL;DR

This paper investigates phase transitions in q-state clock models, revealing that for q=5 the transition differs from the Kosterlitz-Thouless type, and shows how potential modifications can alter the nature of these transitions.

Contribution

It demonstrates that the q=5 clock model exhibits a non-KT transition and that potential modifications can switch the transition type, challenging previous assumptions about these models.

Findings

Helicity modulus does not vanish at the high-temperature transition for q=5.

Modifying the interaction potential changes the transition type.

KT transition can be restored with the Villain potential for q=5.

Abstract

The $q$-state clock model with the cosine potential has a single phase transition for $q\leq4$ and two transitions for $q\geq5$. It is shown by Monte Carlo simulations that the helicity modulus for the five-state clock model ($q=5$) does not vanish at the high-temperature transition. This is in contrast to the clock models with $q\geq6$ for which the helicity modulus vanishes. This means that the transition for the five-state clock model differs from the Kosterlitz-Thouless (KT) transition. It is also shown that this change in the transition is caused by an interplay between the number of angular directions and the interaction potential: by slightly modifying the interaction potential, the KT transition for $q=6$ turns into the same non-KT transition. Likewise, the KT transition is recovered for $q=5$ when the Villain potential is used. Comparisons with other clock-model results are made and discussed.