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Nature of energy transport around a critical point is studied in the Creutzcellular automaton. Fourier heat law is confirmed to hold in this model by adirect measurement of heat flow under a temperature gradient. The thermalconductivity is carefully investigated near the phase transition by the use ofthe Kubo formula. As the result, the thermal conductivity is found to take afinite value at the critical point contrary to some previous works. Equal-timecorrelation of the heat flow is also analyzed by a mean-field typeapproximation to investigate the temperature dependence of thermalconductivity. A variant of the Creutz cellular automaton called the Q2R is alsoinvestigated and similar results are obtained.Comment: 27 pages including 14figure

Transport phenomena at a critical point: Thermal conduction in the Creutz cellular automaton