Bounds on the oscillation of spin system

A birth and death process is used to compare the dynamics of two finite Markov spin systems with different initial configurations. This procedure results in bounds on the oscillation of functionals of the finite spin system as a function of the initial configuration. Such bounds are used, in the one- and two-dimensional cases, to prove the existence of infinite Feller spin systems which do not satisfy T. Liggett's “bounded variation” condition on the interaction functions.