Groupoid C*-algebras, conformal measures and phase transitions

• Ano de defesa: 2018
• Autor(a) principal: Frausino, Rodrigo Souza
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: C*-álgebra; C*-algebras; Conformal measures; Estados KMS; Groupoid; Grupóide; KMS states.; Medidas conformes; Phase transition; Transição de fase
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-11042019-083703/

The objective of this work is the study of phase transitions on the context of Groupoids and their C*-Algebras. The main result of this dissertation is due to Klaus Thomsen in [Tho17], which investigates the connection between conformal measures in the classical formalism and KMS-states in the quantum formalism. The phase transition in the quantum setting is a consequence of this connection between both formalisms and the fact that on the classical setting it was known examples of continuous potentials that show the phenomena of phase transition. The potential used was introduced by Hofbauer [Hof77], an example that shows, dierently from potential of summable variations, potentials only continuous can exhibit phase transition.