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

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.

27 pages, 2 figures. To appear in Ergodic Theory and Dynamical Systems

References in corpus (3)

• Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type
• Chaotic temperature dependence at zero temperature
• Equilibrium states and zero temperature limit on topologically transitive countable Markov shifts

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• Zero-Temperature Chaos in Bidimensional Models with Finite-Range Potentials
• On the selection of subaction and measure for perturbed potentials
• Characterisation of the Set of Ground States of Uniformly Chaotic Finite-Range Lattice Models
• Robust sensitive dependence of geometric Gibbs states for analytic families of quadratic maps