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| Author(s): |
Eric Ossami Endo
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2018-07-31 |
| Examining board members: |
Rodrigo Bissacot Proença;
Aernout Coert Daniel van Enter;
Luiz Renato Goncalves Fontes;
Christof Kuelske;
Arnaud Le Ny
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| Advisor: | Rodrigo Bissacot Proença |
| Abstract | |
In this thesis we study various properties of the spins models, in particular, Ising and Dyson models. We study the stability of the phase transition of the nearest-neighbor ferromagnetic Ising model when we add a perturbation to the critical external field that becomes weaker far from the root of the Cayley tree. We also study the relation between g-measures and Gibbs measures, showing that the Dyson model at sufficiently low temperature is not a g-measure. Counting contours on trees is also studied, showing the characterization of the trees that have infinite number of contours, and comparisons between various definitions of contours. We also study the measures of the spatial Gibbs random graphs, and their local convergence. (AU) | |
| FAPESP's process: | 14/10637-9 - Combinatorial Problems in Ferromagnetic Models |
| Grantee: | Eric Ossami Endo |
| Support Opportunities: | Scholarships in Brazil - Doctorate |