Transport Phenomena at a Critical Point -- Thermal Conduction in the Creutz Cellular Automaton --

TL;DR

This study investigates energy transport at a critical point in the Creutz cellular automaton, confirming Fourier's law and revealing finite thermal conductivity at the phase transition, with analysis extended to a variant model.

Contribution

It provides the first detailed measurement of thermal conductivity near the critical point in the Creutz cellular automaton, demonstrating finite conductivity contrary to previous assumptions.

Findings

Fourier heat law holds in the model.

Thermal conductivity remains finite at the critical point.

Similar results observed in the Q2R automaton variant.

Abstract

Nature of energy transport around a critical point is studied in the Creutz cellular automaton. 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 phase transition by the use of the Kubo formula. As the 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.