The concept of surface tension in statistical mechanics

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...

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Detalhes bibliográficos
Autor: Pereira, João Felipe Rodrigues
Formato: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2024
País:Brasil
Recursos:Universidade de São Paulo (USP)
Repositorio:Biblioteca Digital de Teses e Dissertações da USP
Idioma:inglés
OAI Identifier:oai:teses.usp.br:tde-31052024-103830
Acesso em linha:https://www.teses.usp.br/teses/disponiveis/45/45132/tde-31052024-103830/
Access Level:acceso abierto
Palavra-chave: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
Descrição
Resumo: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.