Approximate FKG inequalities for phase-bound spin systems (opens in new tab)

The FKG inequality is an invaluable tool in monotone spin systems satisfying the FKG lattice condition, which provides positive correlations for all coordinate-wise increasing functions of spins. However, the FKG lattice condition is somewhat brittle and is not preserved when confining a spin system to a particular phase. For instance, consider the Curie-Weiss model, which is a model of a ferromagnet with two phases at low temperature corresponding to positive and negative overall magnetizati...