TY - JOUR

T1 - Transport phenomena at a critical point

T2 - Thermal conduction in the Creutz cellular automaton

AU - Saito, K.

AU - Takesue, S.

AU - Miyashita, S.

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1999

Y1 - 1999

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.

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U2 - 10.1103/PhysRevE.59.2783

DO - 10.1103/PhysRevE.59.2783

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

ER -