FREE ENERGY IN THE MIXED p-SPIN MODELS WITH VECTOR SPINS

• 成果类型: Article
• 署名作者: Panchenko, Dmitry
• 署名单位: University of Toronto
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1194
• 发表日期: 2018
• 页码: 865-896
• 关键词: ghirlanda-guerra identities; mean-field model; sherrington-kirkpatrick model; glass models; parisi ultrametricity; disorder chaos; external-field; systems; bounds; distributions

摘要

Using the synchronization mechanism developed in the previous work on the Potts spin glass model, we obtain the analogue of the Parisi formula for the free energy in the mixed even p-spin models with vector spins, which include the Sherrington-Kirkpatrick model with vector spins interacting through their scalar product. As a special case, this also establishes the sharpness of Talagrand's upper bound for the free energy of multiple mixed p-spin systems coupled by constraining their overlaps.