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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| 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 |
| 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. |
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