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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2024.tde-31052024-103830
Document
Author
Full name
João Felipe Rodrigues Pereira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2024
Supervisor
Committee
Iambartsev, Anatoli (President)
Barata, Joao Carlos Alves
Raszeja, Thiago Costa
Title in English
The concept of surface tension in statistical mechanics
Keywords in English
Contour models
Duality transformations
Pirogov-Sinai theory
Statistical mechanics
Surface tension
Abstract in English
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.
Title in Portuguese
O conceito de tensão superficial em mecânica estatística
Keywords in Portuguese
Mecânica estatística
Modelos de contornos
Tensão superficial
Teoria de Pirogov-Sinai
Transformações de dualidade
Abstract in Portuguese
Nesta dissertação foram estudados dois artigos relacionados à existência e cotas para a tensão superficial Τβ. A teoria de Pirogov-Sinai é utilizada para obter uma cota inferior estritamente positiva para a tensão superficial, mas a existência do limite que define Τβ não é discutida. No caso especial de interações ferromagnéticas para modelos do tipo Ising, onde os acoplamentos J_A são todos não negativos, a existência e uma cota superior uniforme em cada retângulo d-dimensional de lados (L_1, ..., L_d, 2M) para o limite que define Τβ são obtidos por meio de um argumento de superaditividade. Também realizamos um estudo aprofundado das relações de dualidade entre modelos do tipo Ising, necessárias para compreender o argumento.
 
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Dissertacao.pdf (1.19 Mbytes)
Publishing Date
2024-06-11
 
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