Generic scale invariance in classical nonequilibrium systems (invited)

Abstract

Unlike those in equilibrium, dissipative nonequilibrium systems are capable of generic scale invariance-correlations that decay algebraically in space and time for arbitrary parameter values. For one class of such systems, viz., those (such as fluids in a temperature gradient) subjected to external white noise, the existence of a conserved order parameter is believed to be a necessary and almost sufficient condition for generic scale invariance to occur. The evidence for this assertion and the few exceptions, i.e., noisy, conserving nonequilibrium systems with exponential decays of spatial correlations, are discussed using illustrative examples taken from magnetism wherever possible. Simple calculations of exponents characterizing the algebraic decays are shown. A second class of nonequilibrium systems, exemplified by models of sandpiles and earthquakes, which have also been argued to exhibit generic scale invariance, or "self-organized criticality," are briefly discussed. These systems are either noiseless or are subjected to strongly correlated external noise, and include among them at least one apparent magnetic realization. The conditions under which scale invariance can occur in this class, and in particular whether a conservation law is necessary, are still unclear.