Using a weak-disorder scheme and real-space renormalization-group techniques, we obtain analytical results for the critical behavior of various q-state Potts models with correlated disordered exchange interactions along d1 of d spatial dimensions on hierarchical (Migdal-Kadanoff) lattices. Our results indicate qualitative differences between the cases d − d1 = 1 (for which we find nonphysical random fixed points, suggesting the existence of nonperturbative fixed distributions) and d − d1 > 1 (for which we do find acceptable perturbartive random fixed points), in agreement with previous numerical calculations by Andelman and Aharony. We also rederive a criterion for relevance of correlated disorder, which generalizes the usual Harris criterion.
We include p-spin interactions in a spherical version of a soluble mean-field
spin-glass model proposed by van Hemmen. Due to the simplicity of the
solutions, which do not require the use of the replica trick, we are able to
carry out a detailed investigation of a number of special situations. For p
larger or equal to 3, there appear first-order transitions between the
paramagnetic and the ordered phases. In the presence of additional
ferromagnetic interactions, we show that there is no stable mixed phase, with
both ferromagnetic and spin-glass properties.Comment: To appear in Physica
We analyze the critical behavior of a q-state Potts model with correlated disordered ferromagnetic exchange interactions along the layers of a diamond hierarchical lattice. For a special class of weakly disordered distributions, we use the topological properties of the lattice to write a set of recursion relations for the moments of the probability distribution of the interaction parameters. We identify a small parameter, q-q0, where q0=0.537…, to expand and decouple the recursion relations. For q<q0, there is just a trivial stable fixed point, associated with the critical behavior of the uniform model. For q>q0 (that correponds, in a uniform case, to a specific heat critical exponent α>-2), the existence of a stable disordered fixed point indicates a change in the critical behavior. We make some remarks on the validity of the Harris criterion for hierarchical lattices.
Há cerca de cinqüenta anos, numa série pioneira de trabalhos, Mario Schönberg utilizou métodos de segunda quantização para generalizar o teorema de Liouville, introduzindo a idéia de indistinguibilidade entre partículas clássicas. O espaço de Fock, que era considerado um atributo paradigmático dos sistemas quânticos, foi utilizado com rigor matemático e consistência física para construir um formalismo da mecânica estatística clássica descrevendo um sistema com número variável de partículas. Abordagens semelhantes foram redescobertas ao longo das últimas três décadas, em particular no contexto de modelos estocásticos, incluindo processos irreversíveis em redes de spins e reações químicas. Apresentamos uma descrição da teoria de Schönberg, estabelecendo conexões com desenvolvimentos mais recentes. O nosso trabalho é uma contribuição pedagógica, enfatizando a consistência física da utilização da representação número de ocupação em contextos clássicos.
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