  An operator algebra implementation of Markov chain Monte Carlo algorithms for
simulating Markov random fields is proposed. It allows the dynamics of networks
whose nodes have discrete state spaces to be specified by the action of an
update operator that is composed of creation and annihilation operators. This
formulation of discrete network dynamics has properties that are similar to
those of a quantum field theory of bosons, which allows reuse of many
conceptual and theoretical structures from QFT. The equilibrium behaviour of
one of these generalised MRFs and of the adaptive cluster expansion network
(ACEnet) are shown to be equivalent, which provides a way of unifying these two
theories.
