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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 174, Number 2, Pages 228–242
DOI: https://doi.org/10.4213/tmf8400 (Mi tmf8400) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Ultrametricity of the state space in glasses

M. G. Vasina, E. E. Tareevab, T. I. Shchelkachevab, N. M. Shchelkachevcdb

a Physico-Technical Institute, Ural Branch, RAS, Izhevsk, Russia
b Vereshchagin Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia
c Moscow Physico-Technical Institute, Moscow, Russia
d Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia
Full-text PDF (514 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf8400
Abstract: We review the results related to the ultrametricity notion in glasses. We present the proof of the ultrametricity of the replica space for an arbitrary spin glass model with reflection symmetry. We solve the problem of describing the dynamics of a system with an ultrametric state space using the Keldysh functional method for nonequilibrium dynamics in which the quasinonergodicity of the system is taken into account by introducing a hierarchical spectrum of relaxation times.
Keywords: glass, ultrametricity, nonequilibrium dynamics.
Received: 14.08.2012
English version:
Theoretical and Mathematical Physics, 2013, Volume 174, Issue 2, Pages 197–208
DOI: https://doi.org/10.1007/s11232-013-0017-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. G. Vasin, E. E. Tareeva, T. I. Shchelkacheva, N. M. Shchelkachev, “Ultrametricity of the state space in glasses”, TMF, 174:2 (2013), 228–242; Theoret. and Math. Phys., 174:2 (2013), 197–208
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf8400
  • https://doi.org/10.4213/tmf8400
  • https://www.mathnet.ru/eng/tmf/v174/i2/p228
    • This publication is cited in the following 4 articles:
    1. Takada A., Conradt R., Richet P., “Glass Thermodynamics: Clausius Theorem and a New Tensorial Definition of Temperature”, Phys. Chem. Glasses-Eur. J. Glass Sci. Technol. Part B, 62:1 (2021), 8–18  crossref  isi
    2. E. E. Tareeva, T. I. Schelkacheva, N. M. Chtchelkachev, “Some peculiarities in the behavior of non-Ising spin glasses”, Theoret. and Math. Phys., 182:3 (2015), 437–447  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Schelkacheva T.I. Tareyeva E.E. Chtchelkatchev N.M., “Generalized Sherrington-Kirkpatrick Glass Without Reflection Symmetry”, Phys. Rev. E, 89:4 (2014), 042149  crossref  adsnasa  isi  elib  scopus
    4. Tareyeva E.E. Schelkacheva T.I. Chtchelkatchev N.M., “Continuous and Discontinuous Transitions in Generalized P-Spin Glass Models”, J. Phys. A-Math. Theor., 47:7 (2014), 075002  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:677
    Full-text PDF :270
    References:84
    First page:15
     
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