Construction of pure states in mean field models for spin glasses. (English) Zbl 1204.82037
Parisi discovered a solution for the Sherrington-Kirkpatrick model, and an assumption about this result is that it decomposes in pure states. The main contribution of the paper is to clarify this statement, and to determine under which conditions can ulrametricity occur? The main mathematics of the paper refers to sequences of random probability measured defined on balls and to probability in Hilbert space.
Reviewer: Guy Jumarie (Montréal)
MSC:
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
| 60G15 | Gaussian processes |
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
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