Freezing transition in three and two dimensions by the generalized density functional theory

A brief introduction to conventional DFT of 3D freezing is given and some recent results are reviewed. The conventional DFT, however, can not be used in the 2D case, particularly, because it can not describe the hexatic phase -- intermediate phase of 2D melting. We generalize DFT to describe 2D systems and two-stage melting scenario including intermediate hexatic phase. Hexatic phase is characterized by the appearance of bond orientational ordering. Our approach describes this fact in terms of the appearance of nonisotropic part of the two-particle distribution function while one-particle density remains constant. Now we are dealing with the bifurcation of the solution of the equation for the binary distribution function. Microscopic expressions for elastic moduli and the Frank constant of hexatic phase are derived on the base of comparison of distribution functions asymptotic behavior with the results of phenomenological theories. We use our approach for the calculation of the phase boundary between usual isotropic liquid and hexatic phase and slightly modified traditional DFT for the phase boundary between hexatic phase and crystalline solid for a number of 2D systems (hard disks, classical electron crystal, thin superconducting films, Yukawa system etc.)Comment: Lecture given on the International School on Strongly correlated systems and critical phenomena, held in JINR, Dubna (Russia) from August 26 to September 5, 1997. 38 Latex pages, no figure

Classical many-particle distribution functions: some new applications

We present a new purely equilibrium microscopic approach to the description of liquid-glass transition in terms of space symmetry breaking of three- and four-particle distribution functions in the cases of two and three dimensions, respectively. The approach has some features of spin glass theories as well as of density-functional theories of freezing.Comment: Talk presented at the "Bogolyubov Conference: Problems of Theoretical and Mathematical Physics", Moscow-Dubna-Kyiv (September 27 - October 6, 1999), 6 pages of Late

Orientational Phase Transition in solid C_60: Bifurcation Approach

A simple model for the angular dependent interaction between C_60 molecules on the face-centered cubic lattice is proposed. The bifurcations of the solutions of the nonlinear integral equations for orientational distribution functions in the mean field approximation are analyzed and the orientational phase transition in solid C_60 is described. The quantitative results for the orientational phase transition are in accordance with experimental data.Comment: 12 pages of Latex, 1 ps figure, to appear in "Theor.Math.Phys." (Moscow

"Double swallow-tail" singularity and glass-glass transition in a quasibinary system

The system with the square shoulder (SS) potential is considered in the frame of Mode Coupling Theory (MCT) approach. An approximation for the structure factor is used that emphasizes the quasibinary character of the system. The qualitative phase diagram is constructed that includes continuous and discontinuous glass-glass transitions. The phase diagram is governed by two swallow tails connected with two $A_4$ singularities.Comment: 8 pages, 5 figure

Replica Symmetry Breaking in an Axial Model of Quadropolar Glass

We perform the replica symmetry breaking (RSB) in the vicinity of the point of instability of the replica symmetric solution in the model of axial quadrupolar glass. It is shown that the solution with the first stage RSB is stable against the second stage RSB. Although there is no reflection symmetry the 1RSB solution bifurcates continuously from the RS one. These facts mean that our model can not be associated with one of two classes usually considered in spin glass theory.Comment: 13 pages, no figure

New Kinds of Phase Transitions: Transformations in disordered Substances

The transitions in disordered substances are discussed briefly: liquid--liquid phase transitions, liquid--glass transition and the transformations of one amorphous form to another amorphous form of the same substances. A description of these transitions in terms of many--particle conditional distribution functions is proposed. The concept of a hidden long range order is proposed, which is connected with the broken symmetry of higher order distribution functions. The appearance of frustration in simple supercooled Lennard--Jones liquid is demonstrated.Comment: 10 pages, 2 figures. Based on the invited talk presented at the Bogolyubov Conference "Problems of Theoretical and Mathematical Physics", September 2-6, Dubna, Russi

Spin one pp-spin glass: the Gardner transition

We examine the phase diagram of the $p$-spin mean field glass model in the spin one case, that is when $S=0,+1,-1$. For large $p$ the model is solved exactly. The analysis reveals that the phase diagram is in some way similar to that of Ising spins. However, as we show, the quadrupolar regular ordering as well as qudrupolar glass order are present now. The temperature of the Gardner 1RSB -- FRSB transition is obtained explicitly for large $p$. The case of higher spins is discussed briefly.Comment: 9 page

Orientational Phase Transition in Solid C_60: A Model Approach

A simple model for the angular dependent interaction between C_60 molecules in face centered cubic lattice is proposed and analyzed by use of the rigorous bifurcation approach. The quantitative results for the orientational phase transition and the characteristics of the ordered phase are in good agreement with the experimental data.Comment: 4 pages, RevTe

Potts spin glasses with 3, 4 and 5 states near T=TcT=T_c: expanding around the replica symmetric solution

Expansion for the free energy functionals of the Potts spin glass models with 3, 4 and 5 states up to the fourth order in $\delta q_{\alpha \beta }$ around the replica symmetric solution (RS) is investigated using a special quadrupole-like representation. The temperature dependence of the 1RSB order parameters is obtained in the vicinity of the point $T=T_c$ where the RS solution becomes unstable. The crossover from continuous to jumpwise behavior with increasing of number of states is derived analytically. The comparison is made of the free energy expansion for the Potts spin glass with that for other models.Comment: 10 pages, 1 figur

"Spherical" 3-State Potts Spin Glass: Exact Solution

A continuous 3-state Potts model with an analog of spherical constraints is proposed and is shown to have an exact solution in the case of infinite-ranged interactions. "Spherical" 3-state Potts spin glass model is solved using the known properties of a large random matrix. For this model the results are identical to those obtained by the replica approach for replica symmetric solution.Comment: 8 pages, no figure