Distribution of structure factors and phase transitions in a driven lattice gas

Abstract

Using Monte Carlo methods, we study the full distribution of structure factors in the standard driven lattice gas at half filling. The time evolution of the structure factors associated with the two lowest non-trivial wavevectors is used to construct histograms. For saturation drive, at temperatures well above , both are exponentially distributed, but with different widths. These results are well described by a continuum field theory with a dynamics which violates the usual fluctuation dissipation theorem. As T is lowered, one of these distributions remains essentially unaltered. By contrast, the other develops a maximum away from the origin, while staying single-peaked throughout. This behaviour is an unmistakable signal for a continuous transition.