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

Author(s)

Bissacot, Rodrigo ; Garibaldi, Eduardo ; Thieullen, Philippe

• Document type: Journal article
• Source: Ergodic Theory and Dynamical Systems; v. 38, p. 23-pg., 2018-05-01.

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(infinity) and 1(infinity). 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. (AU)

• FAPESP's process: 11/16265-8 - Low dimensional dynamics
• Grantee: Edson Vargas
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/10398-7 - Gibbs measures at zero temperature
• Grantee: Eduardo Garibaldi
• Support Opportunities: Research Grants - Visiting Researcher Grant - International