SERIES EXPANSIONS FOR THE ISING-MODEL COUPLED TO 2 HEAT BATHS

We present an algorithm for generating high- and low-temperature expansions for non-equilibrium steady states in lattice spin models coupled to two thermal baths at different temperatures. For the Ising model on a square lattice with the sublattice temperature ratio alpha = T-a/T-b we construct the high-temperature expansion of energy to order eleven. The estimates of T-c are in good agreement with the exact equilibrium result (at alpha = 1) and the existing Monte-Carlo simulations in non equilibrium cases (alpha = 2 and alpha = infinity).