Correlation inequalities and their applications

Correlation inequalities and their applications to the question of the presence or absence of phase transitions is classical lattice systems are considered. A major part of the known inequalities is obtained as a corollary of a single general theorem.Translated from Itogi Nauki i Tekhniki. Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 16, pp. 5–37, 1979.