THE PARISI FORMULA FOR MIXED p-SPIN MODELS

• 成果类型: Article
• 署名作者: Panchenko, Dmitry
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP800
• 发表日期: 2014
• 页码: 946-958
• 关键词: ghirlanda-guerra identities; glass models; ultrametricity

摘要

The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed p-spin models for even p >= 2 was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi formula for general mixed p-spin models which also include p-spin interactions for odd p. Most of the ideas used in the paper are well known and can now be combined following a recent proof of the Parisi ultrametricity conjecture in.