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

Authors
  • Baek, Seung Ki
  • Minnhagen, Petter
Publication Date
Jan 01, 2010
Identifiers
DOI: 10.1103/PhysRevE.82.031102
OAI: oai:DiVA.org:umu-35750
Source
DiVA - Academic Archive On-line
Keywords
Language
English
License
Green
External links

Abstract

The $q$-state clock model with the cosine potential has a single phasetransition for $q\leq4$ and two transitions for $q\geq5$. It is shown byMonteCarlo simulations that the helicity modulus for the five-state clock model($q=5$) does not vanish at the high-temperature transition. This is incontrast to the clock models with $q\geq6$ for which the helicity modulusvanishes. This means that the transition for the five-state clock modeldiffers from the Kosterlitz-Thouless (KT) transition. It is also shown thatthis change in the transition is caused by an interplay between the numberof angular directions and the interaction potential: by slightly modifyingthe interaction potential, the KT transition for $q=6$ turns into the samenon-KT transition. Likewise, the KT transition is recovered for $q=5$ whenthe Villain potential is used. Comparisons with other clock-model resultsare made and discussed.

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