Existence of the zero temperature limit of equilibrium states on topologically transitive countable Markov shifts

Elmer R. Beltrán, Jorge Littin, Cesar Maldonado +1

Consider a topologically transitive countable Markov shift $\Sigma$ and a summable Markov potential $\varphi$ with finite Gurevich pressure and ${\mathrm{Var}}_1(\varphi )<\infty$. We prove existenc…