Full replica symmetry breaking in generalized mean-field spin glasses with reflection symmetry

Abstract

The analysis of the solution with full replica symmetry breaking in the vicinity of T c 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. The crucial role of the reflection symmetry for the character of phase transition in nonrandom mean-field (MF) models is well known (see, e.g., the textbook [1]). Generally speaking the presence of the terms without reflection symmetry causes the first order phase transition, while in the absence of such terms the transition is of the second order. Usually this result is obtained in the frame of the phenomenological approach based on the Ginzburg-Landau (GL) effective Hamiltonian that can be easily obtained for any Hamiltonian through the Hubbard-Stratanovich identity for the partition function.In the case of random MF models the behavior of systems with reflection symmetry is quite different from those without it. In Ref.[2] this problem was investigated in the frame of replica symmetric (RS) approach. The role of the reflection symmetry for the behavior of RS solution for spin-glass-like MF systems was considered and a kind of symmetry rule for the type of the growing of glass order was formulated: if in the nonrandom (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

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

“…Here θ nRSB are the analogs of (9) for higher stages of RSB (see Ref. 26 for details). Therefore, one of the solutions of this equation is trivial at each RSB-step, and the appearance of the nRSB solution can be regarded as the bifurcation of the trivial (n − 1)RSB solution.…”

“…Writing the free energy as a series over δq αβ near T c (up to the fourth order) we obtain q(x) = cx in the leading approximation [a similar procedure was described in details in Ref. 26].…”

“…Since the model with the operatorsÛ with reflective symmetry ( i.e. Tr Û (2k+1) = 0) exactly the same as the model of the Ising spins [26], for reasons of continuity, we consider operators who have a very small Tr Û (2k+1) .…”

Ультраметричность Пространства Состояний В Стеклах

“…Здесь θ nRSB является аналогом (11) для последующих стадий нарушения репличной симметрии (подробнее см. работу [24]). Следовательно, одно из решений этих уравнений всегда является тривиальным на каждой стадии нарушения симметрии реплик, и появление nRSB-решения может рассматриваться как бифуркация тривиального (n − 1)RSB-решения.…”

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

“…So there is no reflection symmetry. Behavior of this model is significantly different from what one usually has in the case of Ising-like operators [2,3,18,19,20,21,22,23,24,25,26,28]. We have done earlier calculations of 1RSB solution for various values of p that could change continuously [26].…”