The FKG inequality, named after its contributors Fortuin, Kasteleyn, and Ginibre, is a result in probability theory that provides a relationship among joint distributions of certain random variables, particularly in the context of lattice structures, such as spins in statistical mechanics. It is most commonly applied in the study of lattice models in statistical physics, including the Ising model.
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The FKG inequality gives positive association under a log-supermodular probability measure on a finite distributive lattice.