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We propose a toy model to describe in the frame of Mode Coupling Theory multiple glass transitions. The model is based on the postulated simple form for static structure factor as a sum of two delta-functions. This form makes it possible to solve the MCT equations in almost analytical way. The phase diagram is governed by two swallow tails resulting from two A 4 singularities and includes liquid–glass transition and multiple glasses. The diagram has much in common with those of binary and quasibinary systems. [ABSTRACT FROM AUTHOR]

Abstract: We investigate near the point of glass transition the expansion of the free energy corresponding to the generalized Sherrington–Kirkpatrick model with arbitrary diagonal operators standing instead of Ising spins. We focus on the case when is an operator with broken reflection symmetry. Such a consideration is important for understanding the behavior of spin glass-like phases in a number of real physical systems, mainly in orientational glasses in mixed molecular crystals which present just the case. We build explicitly a full replica symmetry breaking (FRSB) solution of the equations for the orientational glass order parameters when the nonsymmetric part of is small. This particular result presents a counterexample in the context of usually adopted conjecture of the absence of FRSB solution in systems with no reflection symmetry. [Copyright &y& Elsevier]

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]

In the framework of the theory, based on the density functional theory of freezing, the melting of the system with Yukawa potential and the hard-disk system with square-well attraction is considered. It is shown that melting scenario crucially depends on the shape of the potential. For the soft-core Yukawa potential melting mainly occurs by means of two continuous transitions, however, there is the critical value of the radius of the potential where the crossover from two continuous to one first-order transition occurs. It should be noted that the first-order transition exists only for very short-range interaction. In the case of hard-core square-well potential situation is more complex, and there are several crossover points, where the melting scenario changes from continuous to first-order transition, and vice versa. [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]

In the framework of the density functional theory of freezing proposed in our previous works, we calculate the phase diagram of two-dimensional system of particles interacting through the repulsive shoulder potential. This potential consists of the hard core and repulsive shoulder of the larger radius. It is shown that at low densities the system melts through the continuous transition in accordance with the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) scenario, while at high densities the conventional first order transition takes place. [ABSTRACT FROM AUTHOR]

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]

The role of reflection symmetry for the character of the appearance of replica-symmetric spin glass state is investigated. It is shown that if in the pure system the transition to the ordered phase is of the second order, then in the corresponding random system the glass regime appears as a result of a phase transition; if the transition in the pure system is of the first order, then in the random system the replica-symmetric glass order parameter grows continuously on cooling; the transition to a nonergodic low-temperature phase is associated with replica symmetry breaking. [Copyright &y& Elsevier]