Response to a twist in systems with Zp symmetry: The two-dimensional p-state clock model

Yuta Kumano, Koji Hukushima, Yusuke Tomita, Masaki Oshikawa

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


We study response to a twist in the two-dimensional p-state clock model, which has the discrete Zp symmetry. The response is measured in terms of helicity modulus, which is usually defined with respect to an infinitesimal twist. However, we demonstrate that such a definition is inappropriate for the clock model. The helicity modulus must be defined with respect to a finite, quantized twist which matches the discrete Zp symmetry of the model. Numerical study of the appropriately defined helicity modulus resolves controversy over the clock model, showing the existence of two Berezinskii-Kosterlitz-Thouless transitions for p>4.

Original languageEnglish
Article number104427
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number10
Publication statusPublished - 2013 Sep 30

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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