Abstract

Consider a topologically transitive countable Markov shift Σ and a summable locally constant potential Φ with finite Gurevich pressure and Var1(Φ) < ∞. We prove the existence of the limit limt→ ∞ μt in the weak∗ topology, where μt is the unique equilibrium state associated to the potential tΦ. In addition, we present examples where the limit at zero temperature exists for potentials satisfying more general conditions.