Abstract
The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand. 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, we prove the Parisi formula.
Highlights
Introduction and main resultsIn the past decades, the Sherrington-Kirkpatrick model [13] of Ising spin glass has been intensively studied with the aim of understanding the strange magnetic behavior of certain alloys
As it is hard to compute the free energy from the Parisi formula, the closely related spherical model was studied by A
Sommers [4]; this model is widely believed to retain the main features of the Ising case, and the analogous Parisi formula admits a more explicit representation for the free energy
Summary
Introduction and main resultsIn the past decades, the Sherrington-Kirkpatrick model [13] of Ising spin glass has been intensively studied with the aim of understanding the strange magnetic behavior of certain alloys. We will establish the Aizenman-Sims-Starr (A.S.S.) scheme and prove the Parisi formula in the spherical model with general mixed p-spin interactions taking the approach of [12].
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