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Soprano Loto, Nahuel (2015)
Publisher: Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires
Languages: Spanish; Castilian
Types: Doctoral thesis
Esta tesis contiene dos partes con un tema en común: en cada una de ellas, estudiamos diferentes modelos de mecánica estadística. En la primera parte, estudiamos modelos diluidos de vecinos próximos con espacio de espines finito, donde el grafo subyacente es un subgrafo aleatorio del reticulado d-dimensional. Más precisamente, proporcionamos condiciones suficientes y necesarias para que ocurra co-existencia de fases mediante técnicas de aglomerado aleatorio. En la segunda parte, estudiamos un modelo del tipo Ising con interacciones de vecinos próximos ferromagnéticas y potencial cuadrático del tipo Kac asociado a un campo externo no-homogéneo. En este caso, probamos que la energía libre y la presión existen y establecemos resultados de grandes desvíos y equivalencia de arreglos. This thesis contains two parts with one topic in common: in each one, we study different statistical-mechanical models. In the first part, we study dilute nearest-neighbour models with finite spin state, being the underlying graph a random subgraph of the d-dimensional lattice. More precisely, we give necessary and sufficient conditions for phase co-existence to occur via random-cluster techniques. In the second part, we study an Ising-type model with ferromagnetic nearest-neighbour interactions and quadratic Kac-type potential associated to an inhomogeneous external field. In this case, we prove that the free energy and the pressure exist and establish large deviation and equivalence of ensembles results. Fil:Soprano Loto, Nahuel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
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