On the Characterization of a Finite Random Field by Conditional Distribution and its Gibbs Form

In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, obtain simple necessary and sufficient conditions for existence uniqueness field with given system one-point conditional distributions. Using axiomatic (without notion potential) definition Hamiltonian, any is Gibbsian. We also apply proposed approach Markov fields.