The Aizenman-Sims-Starr scheme and Parisi formula for mixed p-spin spherical models

Wei-Kuo Chen (University of Chicago)


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.

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Pages: 1-14

Publication Date: October 29, 2013

DOI: 10.1214/EJP.v18-2580


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