Related papers: Potts-Percolation-Gauss Model of a Solid
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The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
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The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…
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The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is…
Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. This approach provides an alternative way of inspecting the…
A microscopic statistical model of a quantum solid is developed, where inside a crystalline lattice there can exist regions of disorder, such as dislocation networks or grain boundaries. The cores of these regions of disorder are allowed…
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Springs are used for a wide range of applications in physics and engineering. Possibly, one of its most common uses is to study the nature of restoring forces in oscillatory systems. While experiments that verify the Hooke's law using…
We extend the model of a 2$d$ solid to include a line of defects. Neighboring atoms on the defect line are connected by ?springs? of different strength and different cohesive energy with respect to the rest of the system. Using the…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
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