Parisi function for the Ising spin glass in cluster approximations

Abstract The Ising spin glass is investigated close to the spin glass transition temperature. Parisi's order parameter function and the de Almeida–Thouless (AT) line are obtained in various cluster approximations. A class of cluster approximations introduced by Baviera, Pasquini, and Serva, the Bethe approximation and cactus approximations are used to study effects of fluctuations on the replica symmetry breaking. Fluctuations seem to cause reduction in the slope of the order parameter function. The locus of the AT line for a cluster approximation changes from that for the Sherrington–Kirkpatrick (SK) model and the change seems to be affected by the existence of a loop in a cluster.