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Mathematical models in equilibrium statistical mechanics describe physicalsystems with many particles interacting with an external force and with oneanother. Gibbs measure is a fundamental concept in this theory. In existingliterature infinite-volume models are constructed as limits of finite modelsand existence of Gibbs measure for them is proven through DLR formalism. Thegeneral existence proofs are quite complicated and involve topology and clusterexpansion.  In this paper we develop a more transparent and more constructive proof ofexistence of infinite Gibbs measure for a particular case of interaction modelat high temperature. The proof is based on a limiting procedure and involvesestimates of series of semi-invariants and graph-related estimates.

Alternative proof of existence of Gibbs measure at high temperature