### 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 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

_{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

**Response to a twist in systems with Z _{p} symmetry : The two-dimensional p-state clock model.** / Kumano, Yuta; Hukushima, Koji; Tomita, Yusuke; Oshikawa, Masaki.

Research output: Contribution to journal › Article

_{p}symmetry: The two-dimensional p-state clock model',

*Physical Review B - Condensed Matter and Materials Physics*, vol. 88, no. 10, 104427. https://doi.org/10.1103/PhysRevB.88.104427

_{p}symmetry: The two-dimensional p-state clock model. Physical Review B - Condensed Matter and Materials Physics. 2013 Sep 30;88(10). 104427. https://doi.org/10.1103/PhysRevB.88.104427

}

TY - JOUR

T1 - Response to a twist in systems with Zp symmetry

T2 - The two-dimensional p-state clock model

AU - Kumano, Yuta

AU - Hukushima, Koji

AU - Tomita, Yusuke

AU - Oshikawa, Masaki

PY - 2013/9/30

Y1 - 2013/9/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84885237616&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885237616&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.88.104427

DO - 10.1103/PhysRevB.88.104427

M3 - Article

VL - 88

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 10

M1 - 104427

ER -