Two-dimensional models in statistical mechanics and a possible approach using ergodic optimization

• Grant number: 11/22423-5
• Support Opportunities: Regular Research Grants
• Start date: April 01, 2012
• End date: March 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Rodrigo Bissacot Proença
• Grantee: Rodrigo Bissacot Proença
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated researchers: Eduardo Garibaldi ; Leandro Martins Cioletti

Abstract

In this project we will study the possible extension of results of the recent area called {\ it Ergodic Optimization} for two-dimensional systems in statistical mechanics. The optimization's techniques are already used in the description of all the Gibbs states of the zero temperature, the measures called {\ it ground states}, the approach ensures the existence (if we are in the non-compact case) and in some situations allows a precise description of all ground states in one-dimensional models. The idea is to get similar results of optimization models in dimension 2 seeking wherever possible to use the results already known for such models in the context of Statistical Mechanics. (AU)

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; CASSANDRO, MARZIO; CIOLETTI, LEANDRO; PRESUTTI, ERRICO. Phase Transitions in Ferromagnetic Ising Models with Spatially Dependent Magnetic Fields. Communications in Mathematical Physics, v. 337, n. 1, p. 41-53, JUL 2015. (11/22423-5)