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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
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.
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