It is shown that one-dimensional Gibbs states may be represented as concatenations of infinite lists of iid "words." It follows that Gibbs states inherit many properties of recurrent Markov chains on denumerable state spaces.
"Regenerative Representation for One-Dimensional Gibbs States." Ann. Probab. 14 (4) 1262 - 1271, October, 1986. https://doi.org/10.1214/aop/1176992367