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

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 multispecies spherical p-spin models, assuming that certain free energies converge. 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 Poincaré 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).