Zero Temperature Limits of Gibbs Equilibrium States for Countable Markov Shifts

We prove that, given a uniformly locally constant potential f on a countable state Markov shift and suitable conditions which guarantee the existence of the equilibrium states μ tf for all t , the measures μ tf converge in the weak star topology as t tends to infinity.

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Bibliographic Details
Published inJournal of statistical physics Vol. 143; no. 4; pp. 795 - 806
Main Author Kempton, Tom
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.05.2011
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Equilibrium state
Countable alphabet Markov shift
Maximizing measure
Gibbs state
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Summary:We prove that, given a uniformly locally constant potential f on a countable state Markov shift and suitable conditions which guarantee the existence of the equilibrium states μ tf for all t , the measures μ tf converge in the weak star topology as t tends to infinity.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-011-0195-x