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arXiv · 1512.08071

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

Rodrigo Bissacot·Eduardo Garibaldi·Philippe Thieullen
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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 locally constant, Lipschitz continuous or, more generally, of summable variation. We assume there exists 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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Rodrigo Bissacot, Eduardo Garibaldi, Philippe Thieullen. 2015-12-26. Zero-temperature phase diagram for double-well type potentials in the summable variation class. https://doi.org/10.1017/etds.2016.57

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