### 抄録

Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D q=5 Potts model and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the three- and four-dimensional XY models and in the 2D q-state Potts models for 2≤q≤4 and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D q=5 and 6 Potts models and propose a quantitative criterion on "weakness" of the first-order phase transition.

元の言語 | English |
---|---|

記事番号 | 062121 |

ジャーナル | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

巻 | 92 |

発行部数 | 6 |

DOI | |

出版物ステータス | Published - 2015 12 10 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### これを引用

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*92*(6), [062121]. https://doi.org/10.1103/PhysRevE.92.062121

**Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the Berezinsky-Kosterlitz-Thouless and weak first-order phase transitions.** / Nonomura, Yoshihiko; Tomita, Yusuke.

研究成果: Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 巻. 92, 番号 6, 062121. https://doi.org/10.1103/PhysRevE.92.062121

}

TY - JOUR

T1 - Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the Berezinsky-Kosterlitz-Thouless and weak first-order phase transitions

AU - Nonomura, Yoshihiko

AU - Tomita, Yusuke

PY - 2015/12/10

Y1 - 2015/12/10

N2 - Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D q=5 Potts model and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the three- and four-dimensional XY models and in the 2D q-state Potts models for 2≤q≤4 and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D q=5 and 6 Potts models and propose a quantitative criterion on "weakness" of the first-order phase transition.

AB - Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D q=5 Potts model and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the three- and four-dimensional XY models and in the 2D q-state Potts models for 2≤q≤4 and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D q=5 and 6 Potts models and propose a quantitative criterion on "weakness" of the first-order phase transition.

UR - http://www.scopus.com/inward/record.url?scp=84951143170&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951143170&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.92.062121

DO - 10.1103/PhysRevE.92.062121

M3 - Article

AN - SCOPUS:84951143170

VL - 92

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 6

M1 - 062121

ER -