### Abstract

We study response to a twist in the two-dimensional p-state clock model, which has the discrete Z_{p} 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 Z_{p} 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 language | English |
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Article number | 104427 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 88 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2013 Sep 30 |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

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## Cite this

Kumano, Y., Hukushima, K., Tomita, Y., & Oshikawa, M. (2013). Response to a twist in systems with Z

_{p}symmetry: The two-dimensional p-state clock model.*Physical Review B - Condensed Matter and Materials Physics*,*88*(10), [104427]. https://doi.org/10.1103/PhysRevB.88.104427