Anisotropic perturbations of the simple symmetric exclusion process : long range correlations

(Received 25 October 1990, accepted in final form 22 January 1991)

Abstract
Consider a lattice spin system in which nearest neighbor spins are exchanged at rates which weakly depend on the neighboring configuration. The system has the same symmetry of the lattice except possibly for lattice rotations. We set up a perturbation expansion for the correlation functions at time t around the simple symmetric exclusion process. Convergence is proven for small t and the formal limit reproduces the usual high temperature expansion in the case of detailed balance. If the system is isotropic, then each term in the expansion is strictly local. If not, then, generically, the two points function has the direction dependence of a quadrupole field and decays only like a power r^-d, where r is the spatial separation and is the dimension.