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Zero-temperature phase diagram for double-well type potentials in the summable variation class

Published online by Cambridge University Press:  19 September 2016

RODRIGO BISSACOT ,
EDUARDO GARIBALDI  and
PHILIPPE THIEULLEN
RODRIGO BISSACOT
Affiliation:
Department of Applied Mathematics, University of Sao Paulo, 05508-090 Sao Paulo, Brazil email rodrigo.bissacot@gmail.com
EDUARDO GARIBALDI
Affiliation:
Department of Mathematics, University of Campinas, 13083-859 Campinas, Brazil email garibaldi@ime.unicamp.br
PHILIPPE THIEULLEN
Affiliation:
Institut de Mathématiques, Université de Bordeaux, CNRS, UMR 5251, F-33405 Talence, France email Philippe.Thieullen@math.u-bordeaux1.fr
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Abstract

We study the zero-temperature limit of the Gibbs measures of a class of long-range potentials on a full shift of two symbols $\{0,1\}$ . These potentials were introduced by Walters as a natural space for the transfer operator. In our case, they are constant on a countable infinity of cylinders and are Lipschitz continuous or, more generally, of summable variation. We assume that there exist exactly two ground states: the fixed points $0^{\infty }$ and $1^{\infty }$ . We fully characterize, in terms of the Peierls barrier between the two ground states, the zero-temperature phase diagram of such potentials, that is, the regions of convergence or divergence of the Gibbs measures as the temperature goes to zero.

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 3 , May 2018 , pp. 863 - 885
Copyright
© Cambridge University Press, 2016 

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