True Widom line for a square-well system.

In the present paper we propose a van der Waals-like model that allows a purely analytical study of fluid properties including the equation of state, phase behavior, and supercritical fluctuations. We take a square-well system as an example and calculate its liquid-gas transition line and supercritical fluctuations. Employing this model allows us to calculate not only the thermodynamic response functions (isothermal compressibility ßT, isobaric heat capacity CP, density fluctuations ζT, and thermal expansion coefficient αT), but also the correlation length in the fluid ξ. It is shown that the bunch of extrema widens rapidly upon departure from the critical point. It seems that the Widom line defined in this way cannot be considered as a real boundary that divides the supercritical region into gaslike and liquidlike regions. As it has been shown recently, a dynamic line on the phase diagram in the supercritical region, namely, the Frenkel line, can be used for this purpose.

Generalized Sherrington-Kirkpatrick glass without reflection symmetry.

We investigate generalized Sherrington-Kirkpatrick glassy systems without reflection symmetry. In the neighborhood of the transition temperature, we, in general, uncover the structure of the glass state building the full-replica-symmetry-breaking solution. A physical example of the explicitly constructed solution is given.

Pressure-induced orientational glass phase in molecular para-hydrogen.

We propose a theoretical description of a possible orientational glass transition in solid molecular para-hydrogen and ortho-deuterium under pressure supposing that they are mixtures of J=0 and J=2 states of molecules. The theory uses the basic concepts and methods of standard spin-glass theory. We expect our orientational glass to correspond to the II' phase of the high-pressure hydrogen phase diagram.

Generalized van der Waals theory of liquid-liquid phase transitions.

In the framework of the thermodynamic perturbation theory for fluids we study how the phase diagram of an isotropic repulsive soft-core attractive potential, where a liquid-liquid phase transition exists in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We show that there are some regions in a potential parameter space where a high-density liquid-liquid critical point can exist in addition to the conventional gas-liquid critical point. It is also found that there is a correlation between the behavior of the phase diagram as a function of width of the repulsive step and the structure of the correlation function of a reference liquid.

Low-temperature phase transition in the three-state Potts glass.

The low-temperature instability of one-step replica symmetry breaking (1RSB) phase in three-state Potts spin glass is obtained explicitly. The temperature of the instability is higher than the temperature where the 1RSB entropy becomes negative. The conjecture of the possibility of the low-temperature full RSB is supported.