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TMF, 2013, Volume 174, Number 2, Pages 228–242 (Mi tmf8400)  

This article is cited in 3 scientific papers (total in 3 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

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

DOI: https://doi.org/10.4213/tmf8400

Full text: PDF file (514 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2013, 174:2, 197–208

Bibliographic databases:

Document Type: Article
Received: 14.08.2012

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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