Approximating partition functions of the two-state spin system

Two-state spin system is a classical topic in statistical physics. We consider the problem of computing the partition function of the system on a bounded degree graph. Based on the self-avoiding tree, we prove the system exhibits strong correlation decay under the condition that the absolute value of inverse temperature is small. Due to strong correlation decay property, an FPTAS for the partition function is presented and uniqueness of Gibbs measure of the two-state spin system on a bounded degree infinite graph is proved, under the same condition. This condition is sharp for Ising model.

► Strong correlation decay holds for two-state spins system under condition that (d−1)tanh(β)<1(d−1)tanh(β)<1.
► An FPTAS is presented for two-state spin system under above condition.
► Gibbs measure of two-state spin system is unique on an infinite graph under above condition.