Author:
BISSACOT RODRIGO,GARIBALDI EDUARDO,THIEULLEN PHILIPPE
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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
13 articles.
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