Correlation inequalities and phase transition in the generalized X‐Y model Available to Purchase

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.