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| Author(s): |
João Felipe Rodrigues Pereira
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2024-04-18 |
| Examining board members: |
Anatoli Iambartsev;
Joao Carlos Alves Barata;
Thiago Costa Raszeja
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| Advisor: | Rodrigo Bissacot Proença |
| Abstract | |
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. (AU) | |
| FAPESP's process: | 22/00748-4 - The concept of surface tension in statistical mechanics |
| Grantee: | João Felipe Rodrigues Pereira |
| Support Opportunities: | Scholarships in Brazil - Master |