Correlation inequalities and phase transition in the generalized X-Y model

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Abstract
Correlation inequalities <σAz>≥0 , <σAzσBz>≥<σAz><σBz> , ∂<σAz>/∂JBz≥0 , and ∂<σAz>/∂JBx≤0 are proved for the generalized X‐Y model with the Hamiltonian of the form H=−Σ(JAzσAz+JAxσAx) , where σAz=ΠjεAσjz , σAx=ΠjεAσjx , JAz≥0,JAx≥0 , A denotes an arbitrary subset of the N lattice points, and σjx , σjz are the Pauli matrices. This yields a simple extension of the Griffiths‐Kelly‐Sherman inequalities to the above quantal system. Applications to phase transitions are also discussed briefly.

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