TAP APPROACH FOR MULTISPECIES SPHERICAL SPIN GLASSES II: THE FREE ENERGY OF THE PURE MODELS

• 成果类型: Article
• 署名作者: Subag, Eliran
• 署名单位: Weizmann Institute of Science
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1605
• 发表日期: 2023
• 页码: 1004-1024
• 关键词: metastable states; order parameters; solvable model; complexity; EQUATIONS; points

摘要

In a companion paper we developed the generalized TAP approach for general multispecies spherical mixed p-spin models. In this paper we use it to compute the limit of the free energy at any temperature for all pure mul-tispecies spherical p-spin models, assuming that certain free energies con-verge. Importantly, the pure multispecies models do not satisfy the convexity assumption on the mixture which was crucial in the recent proofs of the Parisi formula for the multispecies Sherrington-Kirkpatrick model by Barra et al. (Ann. Henri Poincare 16 (2015) 691-708) and Panchenko (Ann. Probab. 43 (2015) 3494-3513) and for the multispecies spherical mixed p-spin models by Bates and Sohn (Electron. J. Probab. 27 (2022) Paper No. 52; Comm. Math. Phys. 394 (2022) 1101-1152).