### Abstract

The nature of energy transport around a critical point is studied in the Creutz cellular automaton. The Fourier heat law is confirmed to hold in this model by a direct measurement of heat flow under a temperature gradient. The thermal conductivity is carefully investigated near the critical point by the use of the Kubo formula. As a result, the thermal conductivity is found to take a finite value at the critical point, contrary to some previous works. Equal-time correlation of the heat flow is also analyzed by a mean-field type approximation to investigate the temperature dependence of thermal conductivity. A variant of the Creutz cellular automaton called the Q2R is also investigated and similar results are obtained.

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

Pages (from-to) | 2783-2794 |

Number of pages | 12 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 59 |

Issue number | 3 PART A |

Publication status | Published - 1999 Mar |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*59*(3 PART A), 2783-2794.

**Transport phenomena at a critical point : Thermal conduction in the Creutz cellular automaton.** / Saitou, Keiji; Takesue, S.; Miyashita, S.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 59, no. 3 PART A, pp. 2783-2794.

}

TY - JOUR

T1 - Transport phenomena at a critical point

T2 - Thermal conduction in the Creutz cellular automaton

AU - Saitou, Keiji

AU - Takesue, S.

AU - Miyashita, S.

PY - 1999/3

Y1 - 1999/3

N2 - The nature of energy transport around a critical point is studied in the Creutz cellular automaton. The Fourier heat law is confirmed to hold in this model by a direct measurement of heat flow under a temperature gradient. The thermal conductivity is carefully investigated near the critical point by the use of the Kubo formula. As a result, the thermal conductivity is found to take a finite value at the critical point, contrary to some previous works. Equal-time correlation of the heat flow is also analyzed by a mean-field type approximation to investigate the temperature dependence of thermal conductivity. A variant of the Creutz cellular automaton called the Q2R is also investigated and similar results are obtained.

AB - The nature of energy transport around a critical point is studied in the Creutz cellular automaton. The Fourier heat law is confirmed to hold in this model by a direct measurement of heat flow under a temperature gradient. The thermal conductivity is carefully investigated near the critical point by the use of the Kubo formula. As a result, the thermal conductivity is found to take a finite value at the critical point, contrary to some previous works. Equal-time correlation of the heat flow is also analyzed by a mean-field type approximation to investigate the temperature dependence of thermal conductivity. A variant of the Creutz cellular automaton called the Q2R is also investigated and similar results are obtained.

UR - http://www.scopus.com/inward/record.url?scp=0033089455&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033089455&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033089455

VL - 59

SP - 2783

EP - 2794

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 3 PART A

ER -