Abstract
The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd p. We establish the Aizenman-Sims-Starr scheme and from this together with many well-known results and Dmitry Panchenko's recent proof on the Parisi ultrametricity conjecture [11], we prove the Parisi formula.
Original language | English (US) |
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Article number | 94 |
Journal | Electronic Journal of Probability |
Volume | 18 |
DOIs | |
State | Published - Oct 29 2013 |
Keywords
- Parisi formula
- Ultrametricity