Long-range spatial correlations for anisotropic zero-range processes

Abstract

The spatial correlations are investigated for a homogeneous system of indistinguishable particles undergoing stochastic anisotropic hopping dynamics on the d-dimensional lattice, d>or=2. The interaction is zero range, i.e. the rate at which particles leave a given site only depends on the occupation number at that site. A series expansion around the independent particle system is given for the equal time correlations and is shown to converge for small times t. The formal t to infinity limiting expansion is analysed termwise from which a quadrupole type decay ( approximately r-d) is derived for the stationary two-points function ( eta (0) eta (r))-( eta (0))2. This phenomenon of self-organized criticality is a direct consequence of the anisotropy causing the system to violate the condition of detailed balance, combined with the conservation law forcing a diffusive decay ( approximately t-d2/) of the temporal correlations.