Correlation Identities, Correlation Inequalities, and Upper Bounds on Critical Temperature of Spin Systems

Abstract

A review on spin correlation functions identities and on rigorous correlation functions inequalities is presented for various spin models. The spin correlation identities are exactly obtained from finite cluster of spins for different models, and the rigorous spin correlation inequalities are presented for the discrete and continuous classical spin models and also for quantum spin models. Through these correlation identities and rigorous inequalities, the upper bounds on critical temperatures are obtained by the decay of the correlation function.