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T. I. Schelkacheva

Publications and source records attributed to T. I. Schelkacheva.

15 recordsLinked to original sources
arXiv2017

Full replica symmetry breaking in p-spin-glass-like systems

It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry breaking glass solution in the case of non-reflective symmetry diagonal operators used instead of Ising spins. As an example, axial quadrupole moments in place of Ising spins are considered and the boundary value $p_{c_{1}}\cong 2.5$ is found.

cond-mat.stat-mech↗
arXiv2015

Spin one $p$-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.

cond-mat.dis-nn↗
arXiv2014

Generalized Sherrington--Kirkpatrick-glass without reflection symmetry

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

cond-mat.stat-mech↗
arXiv2014

Continuous and discontinuous transitions in generalized p-spin glass models

We investigate the generalized p-spin models that contain arbitrary diagonal operators U with no reflection symmetry. We derive general equations that give an opportunity to uncover the behavior of the system near the glass transition at different (continuous) p. The quadrupole glass with J=1 is considered as an illustrating example. It is shown that the crossover from continuous to discontinuous glass transition to one-step replica breaking solution takes place at p=3.3 for this model. For p <2+Δp, where Δp= 0.5 is a finite value, stable 1RSB-solution disappears. This behaviour is strongly different from that of the p-spin Ising glass model.

cond-mat.stat-mech↗
arXiv2013

Orientational glass: full replica symmetry breaking in generalized spin glass-like models without reflection symmetry

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 U standing instead of Ising spins. We focus on the case when U 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 non-symmetric part of U 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.

cond-mat.stat-mech↗
arXiv2011

Replica analysis of the generalized p-spin interaction glass model

We investigate stability of replica symmetry breaking solutions in generalized $p$-spin models. It is shown that the kind of the transition to the one-step replica symmetry breaking state depends not only on the presence or absence of the reflection symmetry of the generalized "spin"-operators $\hat{U}$ but on the number of interacting operators and their individual characteristics.

cond-mat.dis-nn↗
arXiv2010

Potts spin glasses with 3, 4 and 5 states near $T=T_c$: 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 $δq_{αβ}$ 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.

cond-mat.dis-nn↗
arXiv2010

Full versus first stage replica symmetry breaking in spin glasses

A short survey is presented on spin--glass--like states characteristics in complex nonmagnetic systems. We discuss the interplay of the interaction structure and symmetry with the classification scenarios of the replica symmetry breaking. It is shown that the kind of the transition to the nonergodic state depends not only on the presence or absence of the reflection symmetry but on the number of interacting operators and their individual characteristics.

cond-mat.dis-nn↗
arXiv2008

Pressure induced orientational glass phase in molecular para-hydrogen

We propose a theoretical description of 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 the II' phase of the high pressure hydrogen phase diagram.

cond-mat.dis-nn↗
arXiv2006

Orientational glass transition in C_60

We construct a model for qualitative description of the orientational glass transition in C_60 on the spin-glass theory basis. The physical origin of the frustration and the disorder is discussed.

cond-mat.stat-mech↗
arXiv2003

Cluster model of glass transition in simple liquids

On the basis of microscopic statistical mechanics of simple liquids the orientational interaction between clusters consisting of a particle and its nearest neighbors is estimated. It is shown that there are ranges of density and temperature where the interaction changes sign as a function of a radius of a cluster. The model of interacting cubic and icosahedral clusters is proposed and solved in mean-field replica symmetric approximation. It is shown that the glass order parameter grows smoothly upon cooling, the transition temperature being identified with the temperature of the replica symmetry breaking. It is shown that upon cooling a Lennard-Jones system, cubic clusters freeze first. The transition temperature for icosahedral clusters is about ten per cent lower. So the local structure of Lennard-Jones glass in the vicinity of glass transition should be most probably cubic.

cond-mat.dis-nn↗
arXiv2002

Reflection symmetry in mean-field replica-symmetric spin glasses

The role of reflection symmetry breaking for the character of the appearance of replica symmetric spin glass state is investigated. We establish the following symmetry rule for classical systems with one order parameter in the replica symmetric mean field approximation. 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 glass and ordered regimes grow continuously in the random system on cooling.

cond-mat.dis-nn↗
arXiv2002

Quadrupolar Glass State in para-hydrogen and ortho-deuterium under pressure

The main features of the possible quadrupolar glass state in ortho-deuterium and para-hydrogen under high pressure are predicted and considered in replica-symmetric approximation in analogy with glassy behavior of diluted ortho-hydrogen at low pressures. The quadrupolar model with J = 2 is suggested. The orientational order and glass regime grow continuously on cooling just as it is in the case of ortho-para hydrogen mixtures at zero pressure.

cond-mat.stat-mech↗
arXiv1998

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.

cond-mat↗