On the TAP equations via the cavity approach in the generic mixed $p$-spin models

Abstract

In 1977, Thouless, Anderson, and Palmer (TAP) derived a system of consistent equations in terms of the effective magnetization in order to study the free energy in the Sherrington-Kirkpatrick (SK) spin glass model. The solutions to their equations were predicted to contain vital information about the landscapes in the SK Hamiltonian and the TAP free energy and moreover have direct connections to Parisi's replica ansatz. In this work, we aim to investigate the validity of the TAP equations in the generic mixed $p$-spin model. By utilizing the ultrametricity of the overlaps, we show that the TAP equations are asymptotically satisfied by the conditional local magnetizations on the asymptotic pure states.

arXiv comment41 pages

References in corpus (12)

• The dynamics of message passing on dense graphs, with applications to compressed sensing
• Statistical physics of inference: Thresholds and algorithms
• Phase transitions and sample complexity in Bayes-optimal matrix factorization
• The Parisi formula has a unique minimizer
• The Parisi formula for mixed $p$-spin models
• Approximate Ultrametricity for Random Measures and Applications to Spin Glasses
• On the TAP free energy in the mixed $p$-spin models
• Thouless-Anderson-Palmer equations for the generic p-spin glass model
• The generalized TAP free energy II
• The TAP-Plefka variational principle for the spherical SK model
• On convergence of the cavity and Bolthausen's TAP iterations to the local magnetization
• On spin distributions for generic p-spin models

Cited by in corpus (1)

• Random projections beyond zero overlap