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arXiv · 1307.5512

Residual discrete symmetry of the five-state clock model

Seung Ki Baek·Harri Mäkelä·Petter Minnhagen·Beom Jun Kim
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Abstract

It is well-known that the $q$-state clock model can exhibit a Kosterlitz-Thouless (KT) transition if $q$ is equal to or greater than a certain threshold, which has been believed to be five. However, recent numerical studies indicate that helicity modulus does not vanish in the high-temperature phase of the five-state clock model as predicted by the KT scenario. By performing Monte Carlo calculations under the fluctuating twist boundary condition, we show that it is because the five-state clock model does not have the fully continuous U(1) symmetry even in the high-temperature phase while the six-state clock model does. We suggest that the upper transition of the five-state clock model is actually a weaker cousin of the KT transition so that it is $q \ge 6$ that exhibits the genuine KT behavior.

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Seung Ki Baek, Harri Mäkelä, Petter Minnhagen, Beom Jun Kim. 2013-07-21. Residual discrete symmetry of the five-state clock model. https://doi.org/10.1103/physreve.88.012125

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