Spin-glass-type state in complex nonmagnetic systems

Tareyeva, E. E.; Schelkacheva, T. I.; Chtchelkatchev, N. M.

doi:10.1007/s11232-009-0110-7

Cited by 14 publications

(22 citation statements)

References 36 publications

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“…If operatorsÛ do not have the reflection symmetry then the nontrivial solution for the regular order parameter x appears in spite of the fact that x is absent inθ (since (2)) [16,17]. The heat capacity can be expressed through the glass order parameters:…”

Section: Main Equationsmentioning

confidence: 99%

Replica analysis of the generalizedp-spin interaction glass model

Schelkacheva¹,

Chtchelkatchev²

2011

J. Phys. A: Math. Theor.

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Abstract. 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"-operatorsÛ but on the number of interacting operators and their individual characteristics.Replica analysis of the generalized p-spin interaction glass model. 2

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Section: Main Equationsmentioning

confidence: 99%

Replica analysis of the generalizedp-spin interaction glass model

Schelkacheva¹,

Chtchelkatchev²

2011

J. Phys. A: Math. Theor.

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“…In such a way a number of real physical systems can be described, see, e.g. the reviews [33,35]. The operators have different physical origin depending on the problem under study.…”

Section: Introductionmentioning

confidence: 99%

Continuous and discontinuous transitions in generalizedp-spin glass models

Tareyeva

Schelkacheva

Chtchelkatchev

2014

J. Phys. A: Math. Theor.

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We investigate the generalized p-spin models that contain arbitrary diagonal operatorsÛ 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 + ∆p, where ∆p = 0.5 is a finite value, stable 1RSB-solution disappears. This behaviour is strongly different from that of the p-spin Ising glass model.

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“…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].…”

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confidence: 89%

“…For T < T 0 we have Almeida-Thoulles replicon mode λ (RS) repl < 0 and RS-solution becomes unstable. Similarly, when T < T 0 we have λ (1RSB) repl < 0 determining the condition when the 1RSB glass is unstable [19,24,26,27].…”

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confidence: 98%

“…Replacing the simple Ising spins by more complex operatorsÛ dramatically expands the range of solvable tasks. The operatorÛ can be, for example, the axial quadrupole moment (quadrupole glass in molecular solid hydrogen at different pressures) or the role ofÛ can be played by certain combinations of the cubic harmonics (orientational glass of the clusters, for example, in C 60 in a wide pressure range), see [18,19,20,21,22,23,24,25,26].…”

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

Schelkacheva

Chtchelkatchev

2017

Jetp Lett.

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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 pc 1 ∼ = 2.5 is found.Introduction The basis of understanding glasses is the Sherrington -Kirkpatrick (SK) model [1]: the Ising model with random links. A stable solution for SK model was obtained by Parisi [2, 3] with a full replica symmetry breaking (FRSB) scheme. Later it was realised that replica symmetry is not abstract and academic question but it corresponds to formation of the specific hierarchy of basins in the energy landscape of the glass forming system.

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Spin-glass-type state in complex nonmagnetic systems

Cited by 14 publications

References 36 publications

Replica analysis of the generalizedp-spin interaction glass model

Replica analysis of the generalizedp-spin interaction glass model

Continuous and discontinuous transitions in generalizedp-spin glass models

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

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