### Abstract

We investigate the critical short-time scaling of the two-dimensional lattice φ^{4} field theory with a Langevin dynamics. Starting from a "hot" initial configuration but with a small magnetization, the critical initial increase of the magnetization is observed, through which we determine the critical point. From the short-time relaxation dynamics of various quantities at the critical point obtained, the dynamic critical exponents θ, z and the static exponent β/ν are evaluated. In executing a Langevin simulation, an appropriate discretization method with respect to the time degree of freedom becomes essentially important to be adopted and we show that the well-known second-order form of discretized Langevin equation works well to investigate the short-time dynamics.

Original language | English |
---|---|

Pages (from-to) | 735-745 |

Number of pages | 11 |

Journal | International Journal of Modern Physics C |

Volume | 20 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2009 May |

### Fingerprint

### Keywords

- φ theory
- Critical phenomena
- Higher-order algorithm
- Langevin dynamics
- Short-time scaling

### ASJC Scopus subject areas

- Computer Science Applications
- Computational Theory and Mathematics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

^{4}theory on the basis of a higher-order algorithm.

*International Journal of Modern Physics C*,

*20*(5), 735-745. https://doi.org/10.1142/S0129183109013959

**Analysis of critical short-time langevin dynamics in two-dimensional φ ^{4} theory on the basis of a higher-order algorithm.** / Otobe, Tsuyoshi; Nakazato, Hiromichi; Okano, Keisuke; Yuasa, Kazuya; Hattori, Nozomu.

Research output: Contribution to journal › Article

^{4}theory on the basis of a higher-order algorithm',

*International Journal of Modern Physics C*, vol. 20, no. 5, pp. 735-745. https://doi.org/10.1142/S0129183109013959

^{4}theory on the basis of a higher-order algorithm. International Journal of Modern Physics C. 2009 May;20(5):735-745. https://doi.org/10.1142/S0129183109013959

}

TY - JOUR

T1 - Analysis of critical short-time langevin dynamics in two-dimensional φ4 theory on the basis of a higher-order algorithm

AU - Otobe, Tsuyoshi

AU - Nakazato, Hiromichi

AU - Okano, Keisuke

AU - Yuasa, Kazuya

AU - Hattori, Nozomu

PY - 2009/5

Y1 - 2009/5

N2 - We investigate the critical short-time scaling of the two-dimensional lattice φ4 field theory with a Langevin dynamics. Starting from a "hot" initial configuration but with a small magnetization, the critical initial increase of the magnetization is observed, through which we determine the critical point. From the short-time relaxation dynamics of various quantities at the critical point obtained, the dynamic critical exponents θ, z and the static exponent β/ν are evaluated. In executing a Langevin simulation, an appropriate discretization method with respect to the time degree of freedom becomes essentially important to be adopted and we show that the well-known second-order form of discretized Langevin equation works well to investigate the short-time dynamics.

AB - We investigate the critical short-time scaling of the two-dimensional lattice φ4 field theory with a Langevin dynamics. Starting from a "hot" initial configuration but with a small magnetization, the critical initial increase of the magnetization is observed, through which we determine the critical point. From the short-time relaxation dynamics of various quantities at the critical point obtained, the dynamic critical exponents θ, z and the static exponent β/ν are evaluated. In executing a Langevin simulation, an appropriate discretization method with respect to the time degree of freedom becomes essentially important to be adopted and we show that the well-known second-order form of discretized Langevin equation works well to investigate the short-time dynamics.

KW - φ theory

KW - Critical phenomena

KW - Higher-order algorithm

KW - Langevin dynamics

KW - Short-time scaling

UR - http://www.scopus.com/inward/record.url?scp=67650784442&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650784442&partnerID=8YFLogxK

U2 - 10.1142/S0129183109013959

DO - 10.1142/S0129183109013959

M3 - Article

VL - 20

SP - 735

EP - 745

JO - International Journal of Modern Physics C

JF - International Journal of Modern Physics C

SN - 0129-1831

IS - 5

ER -