The concept of surface tension in statistical mechanics

• Ano de defesa: 2024
• Autor(a) principal: Pereira, João Felipe Rodrigues
• 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: Contour models; Duality transformations; Mecânica estatística; Modelos de contornos; Pirogov-Sinai theory; Statistical mechanics; Surface tension; Tensão superficial; Teoria de Pirogov-Sinai; Transformações de dualidade
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-31052024-103830/

In this thesis two papers were studied, concerning the existence and bounds for the surface tension Τβ. Pirogov-Sinai theory is employed to yield a strictly positive lower bound to the surface tension, but the existence of the limit defining Τβ is not discussed. In the special case of ferromagnetic interactions for Ising-like models, where the couplings J_A are all non-negative, the existence and a uniform upper bound in each d-dimensional rectangle of sides (L_1, ..., L_d, 2M) to the limit defining Τβ are obtained, by a superadditivity argument. We also make an in-depth study of duality relations between Ising-like models, necessary to understand the argument.