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TMF, 2015, Volume 182, Number 3, Pages 500–512 (Mi tmf8793)  

This article is cited in 2 scientific papers (total in 2 papers)

Some peculiarities in the behavior of non-Ising spin glasses

E. E. Tareevaa, T. I. Schelkachevaa, N. M. Chtchelkachevb

a Vereshchagin Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: This paper is a review. We outline the main directions in the modern theory of spin glasses. The main content is based on our recent papers, devoted to studying replica symmetry breaking in non-Ising spin glasses. Studying a series of generalized models showed a certain uniformity of the behavior of these generalized spin glasses. Essentially, we observe a significant difference between their behavior and the behavior of the known systems with random couplings of Ising spins—the Sherrington–Kirkpatrick model and the corresponding $p$-spin model. We find the bifurcation point for the solution with the first replica symmetry breaking, study the form and stability of the solution near the bifurcation point, and show in which cases the transition to the glass state occurs continuously and in which cases, with a jump of the order parameters.

Keywords: spin glass, quadrupole glass, replica method, Potts model, solution bifurcation

Funding Agency Grant Number
Russian Science Foundation 14-22-00093
14-12-01185
Russian Foundation for Basic Research 14-02-00451


DOI: https://doi.org/10.4213/tmf8793

Full text: PDF file (623 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 182:3, 437–447

Bibliographic databases:

Received: 15.09.2014

Citation: E. E. Tareeva, T. I. Schelkacheva, N. M. Chtchelkachev, “Some peculiarities in the behavior of non-Ising spin glasses”, TMF, 182:3 (2015), 500–512; Theoret. and Math. Phys., 182:3 (2015), 437–447

Citation in format AMSBIB
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\by E.~E.~Tareeva, T.~I.~Schelkacheva, N.~M.~Chtchelkachev
\paper Some peculiarities in the~behavior of non-Ising spin glasses
\jour TMF
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\vol 182
\issue 3
\pages 500--512
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\jour Theoret. and Math. Phys.
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\pages 437--447
\crossref{https://doi.org/10.1007/s11232-015-0272-4}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. JETP Letters, 105:4 (2017), 232–237  mathnet  crossref  crossref  isi  elib
    2. E. E. Tareeva, T. I. Schelkacheva, “Spin-one $p$-spin glass: Exact solution for large $p$”, Theoret. and Math. Phys., 194:2 (2018), 252–259  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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