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Abstract: The analysis of the solution with full replica symmetry breaking in the vicinity of of a general spin glass model with reflection symmetry is performed. The leading term in the order parameter function expansion is obtained. Parisi equation for the model is written. [Copyright &y& Elsevier]

Abstract: A new class of exactly solvable models is proposed: continuous Potts models with an analog of spherical constraints. The “spherical” 3-state Potts spin glass model is solved using the known properties of large random matrices. For this model, the results are identical to those obtained by the replica approach for replica symmetric solution. [Copyright &y& Elsevier]

On the basis of microscopic statistical mechanics of simple liquids an orientational interaction between clusters consisting of a particle and its nearest neighbors is estimated. It is shown that the intercluster interaction drastically depends on density, temperature and radius of a cluster. The model of interacting cubic and icosahedral clusters is proposed for description of structural glasses and is solved in mean-field replica symmetric approximation. Under cooling of the Lennard–Jones system icosahedral clusters freeze first forming bond orientational order; at lower temperatures cubic clusters freeze and form orientational glass phase. [Copyright &y& Elsevier]