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Ultrametricity of the state space in glasses

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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.

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Authors and Affiliations

  1. Physico-Technical Institute, Ural Branch, RAS, Izhevsk, Russia

    M. G. Vasin

  2. Vereshchagin Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia

    E. E. Tareyeva, T. I. Shchelkacheva & N. M. Shchelkatchev

  3. Moscow Physico-Technical Institute, Moscow, Russia

    N. M. Shchelkatchev

  4. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia

    N. M. Shchelkatchev

Authors
  1. M. G. Vasin
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  2. E. E. Tareyeva
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  3. T. I. Shchelkacheva
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  4. N. M. Shchelkatchev
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Correspondence to M. G. Vasin.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 174, No. 2, pp. 228–242, February, 2013.

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Vasin, M.G., Tareyeva, E.E., Shchelkacheva, T.I. et al. Ultrametricity of the state space in glasses. Theor Math Phys 174, 197–208 (2013). https://doi.org/10.1007/s11232-013-0017-1

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