### Abstract

We study phase transition in the ferromagnetic Potts model with invisible states that are added as redundant states by mean-field calculation and Monte Carlo simulation. Invisible states affect the entropy and free energy, although they do not contribute to the internal energy. A second-order phase transition takes place at finite temperature in the standard q-state ferromagnetic Potts model on two-dimensional lattice for q = 2,3, and 4. However, our present model on two-dimensional lattice undergoes a first-order phase transition with spontaneous q-fold symmetry breaking (q = 2,3, and 4) due to entropy effect of invisible states. The model is fundamental for the analysis of a first-order phase transition with spontaneous discrete symmetry breaking.

Original language | English |
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Pages (from-to) | 381-388 |

Number of pages | 8 |

Journal | Progress of Theoretical Physics |

Issue number | 2 |

Publication status | Published - 2010 Aug |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Progress of Theoretical Physics*, (2), 381-388.

**Phase transition in potts model with invisible states.** / Tamura, Ryo; Tanaka, Shu; Kawashima, Naoki.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, no. 2, pp. 381-388.

}

TY - JOUR

T1 - Phase transition in potts model with invisible states

AU - Tamura, Ryo

AU - Tanaka, Shu

AU - Kawashima, Naoki

PY - 2010/8

Y1 - 2010/8

N2 - We study phase transition in the ferromagnetic Potts model with invisible states that are added as redundant states by mean-field calculation and Monte Carlo simulation. Invisible states affect the entropy and free energy, although they do not contribute to the internal energy. A second-order phase transition takes place at finite temperature in the standard q-state ferromagnetic Potts model on two-dimensional lattice for q = 2,3, and 4. However, our present model on two-dimensional lattice undergoes a first-order phase transition with spontaneous q-fold symmetry breaking (q = 2,3, and 4) due to entropy effect of invisible states. The model is fundamental for the analysis of a first-order phase transition with spontaneous discrete symmetry breaking.

AB - We study phase transition in the ferromagnetic Potts model with invisible states that are added as redundant states by mean-field calculation and Monte Carlo simulation. Invisible states affect the entropy and free energy, although they do not contribute to the internal energy. A second-order phase transition takes place at finite temperature in the standard q-state ferromagnetic Potts model on two-dimensional lattice for q = 2,3, and 4. However, our present model on two-dimensional lattice undergoes a first-order phase transition with spontaneous q-fold symmetry breaking (q = 2,3, and 4) due to entropy effect of invisible states. The model is fundamental for the analysis of a first-order phase transition with spontaneous discrete symmetry breaking.

UR - http://www.scopus.com/inward/record.url?scp=78649644157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649644157&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:78649644157

SP - 381

EP - 388

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 2

ER -