Chaos and Turing machines on bidimensional models at zero temperature

• Autor(a) principal: Nosaki, Gregorio Luis Dalle Vedove
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-04012021-102503/
• topic: Equilibrium measure; Formalismo termodinâmico; Medida de equilíbrio; Subshift; Subshift; Thermodynamic formalism

In equilibrium statistical mechanics or thermodynamics formalism one of the main objectives is to describe the behavior of families of equilibrium measures for a potential parametrized by the inverse temperature beta. Here we consider equilibrium measures as the shift invariant measures that maximizes the pressure. Other constructions already prove the chaotic behavior of these measures when the system freezes. One of the most important examples was given by Chazottes and Hochman where they prove the non-convergence of the equilibrium measures for a locally constant potential when the dimension is bigger than or equal to 3. In this work we present a construction of a bidimensional example described by a finite alphabet and a locally constant potential in which there exists a subsequence where the non-convergence occurs for any sequence of equilibrium measures at inverse temperatures beta. In order to describe such an example, we use the construction described by Aubrun and Sablik which improves the result of Hochman used in the construction of Chazottes and Hochman.