Ultrametricity of the state space in glasses. (English. Russian original) Zbl 1281.82032
Theor. Math. Phys. 174, No. 2, 197-208 (2013); translation from Teor. Mat. Fiz. 174, No. 2, 228-242 (2013).
Summary: 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.
MSC:
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
| 82C44 | Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics |
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