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ABSTRACT: Expansion for the 1RSB free energy functionals of the mean-field (MF) Potts spin glass models up to the fourth order in δqαβ around the replica symmetric (RS) solution is investigated. We consider models with three, four and five states and use a special quadrupole-like representation for them. The corresponding series for the 1RSB order parameters giving explicit temperature dependence are obtained in the vicinity of the point T = Tc, where the RS solution becomes unstable. The crossover from continuous to jumpwise behavior with increasing number of states is derived analytically. A comparison is made between the free energy expansion for the Potts spin glass and that for other models.
Journal of Physics A Mathematical and Theoretical 11/2010; 43(49):495006. · 1.56 Impact Factor
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ABSTRACT: 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.
07/2010;
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ABSTRACT: This paper presents a simulation study of the applicability of the Rosenfeld entropy scaling to the systems which cannot be approximated by the effective hard spheres. Three systems are studied: the Herzian spheres, the Gauss core model, and a soft repulsive shoulder potential. These systems demonstrate diffusion anomalies at low temperatures: the diffusion coefficient increases with increasing density or pressure. It is shown that for the first two systems belonging to a class of bounded potentials, the Rosenfeld scaling formula is valid only in the infinite-temperature limit where there are no anomalies. For the soft repulsive shoulder potential, the scaling formula is valid already at sufficiently low temperatures, however, out of the anomaly range.
Physical Review E 06/2010; 81(6 Pt 1):061201. · 2.26 Impact Factor
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ABSTRACT: We report a computer-simulation study of the equilibrium phase diagram of a three-dimensional system of particles with a repulsive-shoulder potential. The phase diagram was obtained using free-energy calculations. At low temperatures, we observe a number of distinct crystal phases. We show that at certain values of the potential parameters the system exhibits the waterlike thermodynamic anomalies: a density anomaly and a diffusion anomaly. The anomalies disappear with increasing the repulsive step width: more precisely, their locations move to the region where the crystalline phase is stable.
Physical Review E 06/2009; 79(5 Pt 1):051202. · 2.26 Impact Factor
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ABSTRACT: We report a computer-simulation study of the equilibrium phase diagram of a three-dimensional system of particles with a repulsive step potential. The phase diagram is obtained using free-energy calculations. At low temperatures, we observe a number of distinct crystal phases. We show that at certain values of the potential parameters the system exhibits the water-like thermodynamic anomalies: density anomaly and diffusion anomaly. The anomalies disappear with increasing the repulsive step width: their locations move to the region inside the crystalline phase. Comment: 6 pages, 5 figures
12/2008;
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ABSTRACT: We report a computer-simulation study of the equilibrium phase diagram of a three-dimensional system of particles with a repulsive-step potential. Using free-energy calculations, we have determined the equilibrium phase diagram of this system. At low temperatures, we observe a number of distinct crystal phases. However, under certain conditions the system undergoes a glass transition in a regime where the liquid appears thermodynamically stable. We argue that the appearance of this amorphous low-temperature phase can be understood by viewing this one-component system as a quasibinary mixture.
The Journal of chemical physics 09/2008; 129(6):064512. · 3.09 Impact Factor
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ABSTRACT: The comprehensive computer simulation study of the phase diagram of the repulsive step potential system in three dimensions is represented. We show that the system with a simple purely repulsive isotropic potential demonstrates a number of unusual features. The maxima and minima on the melting curve are found for some regions of potential parameters. It is shown that the phase diagram in $\rho-T$ plane includes two isostructural crystalline parts separated by the disordered phase which is amorphous at low enough temperatures. Phase diagram in the (P-T) plane shows that the transition to the amorphous state occurs approximately along the extrapolated spinodals. Structural FCC-BCC phase transition is found at high densities.
01/2007;
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ABSTRACT: 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.
05/2004;
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ABSTRACT: 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.
Physical Review E 01/2004; 68(6 Pt 2):067103. · 2.26 Impact Factor
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ABSTRACT: The low-temperature instability of one-step replica symmetry breaking (1RSB) phase in 3-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. Comment: 8 pages, 2 figures
07/2003;
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ABSTRACT: 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. Comment: 6 pages, 2 figures
11/2002;
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ABSTRACT: We investigate the replica symmetry breaking (RSB) in a neighborhood of the instability point of the replica-symmetric solution in the axial quadrupolar glass model. We show that the solution with the first-stage RSB is stable against the subsequent RSB. Although there is no reflection symmetry, the first-stage RSB solution continuously bifurcates from the replica-symmetric one. This implies that our model does not belong to either of the two classes into which spin glasses are usually divided.
Theoretical and Mathematical Physics 05/2002; 131(3):852-861. · 0.65 Impact Factor
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ABSTRACT: 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.
05/2002;
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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.
Physics Letters A.
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ABSTRACT: 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.
Physics Letters A.
