TAP approach for multi-species spherical spin glasses I: general theory

2021/11/13 by Subag, Eliran · 3 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.07132

Abstract

We develop a generalized TAP approach for the multi-species version of the spherical mixed p-spin models. In particular, we prove a generalized TAP representation for the free energy at any overlap vector which is multi-samplable in an appropriate sense. Moreover, we show that if a multi-samplable overlap is maximal, then the TAP correction is equal to an analogue of the well-known Onsager reaction term. Finally, in a companion paper we use the results from the current paper to compute the free energy at any temperature for all multi-species pure p-spin models, assuming the free energy converges.

Cited by

• Spin glasses and the Parisi formula
• Ground state energies of multipartite p-spin models -- partially lifted RDT view
• Balanced multi-species spin glasses

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