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Gibbs measures at zero temperature

Grant number: 15/10398-7
Support Opportunities:Research Grants - Visiting Researcher Grant - International
Start date: October 04, 2015
End date: October 31, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Eduardo Garibaldi
Grantee:Eduardo Garibaldi
Visiting researcher: Philippe Thieullen
Visiting researcher institution: Université Bordeaux 1, France
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM

Abstract

The main challenge in the study of freezing phenomena for Gibbs states is to interpret the often complicated entropy behaviour dictated by the associated maximizing probabilities. Actually, the fundamental questions on the recognition of non-convergence of Gibbs measures for exponentially decreasing interactions remain open. In this context, it is particularly challenging to characterize and classify in a qualitative way the non-convergence phenomena and to develop an algorithmic approach for this analysis. Our general goals during this research visit consist thus in developing tools in the freezing process of Gibbs states from a mathematical viewpoint, which have a potential impact on the equilibrium statistical mechanics. Recalling that the maximizing measures are those invariant probabilities whose support lies on the associated Aubry set, a particular problem to be analyse will be the construction of an explicit example for non-convergence of Gibbs measures when the corresponding Aubry set has zero topological entropy. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BISSACOT, RODRIGO; GARIBALDI, EDUARDO; THIEULLEN, PHILIPPE. Zero-temperature phase diagram for double-well type potentials in the summable variation class. Ergodic Theory and Dynamical Systems, v. 38, n. 3, p. 863-885, . (11/16265-8, 15/10398-7)
BISSACOT, RODRIGO; GARIBALDI, EDUARDO; THIEULLEN, PHILIPPE. Zero-temperature phase diagram for double-well type potentials in the summable variation class. Ergodic Theory and Dynamical Systems, v. 38, p. 23-pg., . (11/16265-8, 15/10398-7)