Spin glass withS=1

Luchinskaya, E. A.; Tareeva, E. E.

doi:10.1007/bf01028443

Cited by 6 publications

(9 citation statements)

References 12 publications

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“…In this case, the problem becomes completely similar to that in the case of spin glass with S = 1 [31]. Otherwise, there are no trivial solutions of the equations for the order parameters; they increase continuously as the temperature decreases.…”

Section: Role Of the Reflection Symmetrymentioning

confidence: 83%

Spin-glass-type state in complex nonmagnetic systems

2009

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Section: Role Of the Reflection Symmetrymentioning

confidence: 83%

Spin-glass-type state in complex nonmagnetic systems

2009

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“…Such a phenomenon was first encountered in generalized SK [3] model for spin one case investigated in RS approximation in the paper Ref. [24]. After performing high-temperature series expansion of the RS equations Eq.…”

Section: Large P Solution the Existence Of The Quadrupole Glassmentioning

confidence: 91%

Spin one $p$-spin glass: the Gardner transition

Schelkacheva,

Tareyeva

2015

Preprint

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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.

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“…Here η > 0 is a tuning parameter. The behavior of the system is quite different in the cases η = 1/ √ 3 (analog of spin-one glass model [15]) and η = 1/ √ 3.…”

Section: As An Example Let Us Consider the Hamiltonian (1) Withmentioning

confidence: 99%

“…Here θ0 = t The indices in (15) are different only if they are connected through δq αβ . We believe that the parameter p (5) changes slowly and is equal to p c in the vicinity of t c .…”

Section: As An Example Let Us Consider the Hamiltonian (1) Withmentioning

confidence: 99%

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

2006

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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

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Spin glass withS=1

Cited by 6 publications

References 12 publications

Spin-glass-type state in complex nonmagnetic systems

Spin-glass-type state in complex nonmagnetic systems

Spin one $p$-spin glass: the Gardner transition

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

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