  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, we
obtain simple necessary and sufficient conditions for the existence and
uniqueness of a finite random field with a given system of one-point
conditional distributions. Using the axiomatic (without the notion of
potential) definition of Hamiltonian, we show that any finite random field is
Gibbsian. We also apply the proposed approach to Markov random fields.
