The global Markov property for equilibrium states which are determined by correlations in a strip
Consider an interaction-round-face potential on the lattice \({\mathbb{Z}}^ d\), which may include nearest-neighbor and next-nearest-neighbor pair interactions, as well as more general plaquette terms. Assuming some periodicity of the potential it is shown that, under the condition that equilibrium states can be distinguished by expectation values of sufficiently local observables, equilibrium states possess a global Markov property. The condition under which this Markov property is shown to hold is met in particular in case the equilibrium state is unique or determined by the magnetization. The proof is based on an application of the variational principle to states which are constructed like Markov chains.
nearest-neighbor and next-nearest-neighbor pair interactions
scientific article; zbMATH DE number 4043021