Non-Convex Multipartite Ferromagnets

Abstract

We investigate a multipartite ferromagnetic model without self-interactions between spins of the same party, so that the Hamiltonian is not a definite quadratic form of the magnetisations. We find the free energy and study the phase transition for all zero external fields. Moreover in the bipartite case we analyse the fluctuations of the rescaled magnetisations, below and at the critical point, and we study the phase transitions with non zero magnetic fields.

17 pages, 5 figures

References in corpus (2)

• The free energy in a multi-species Sherrington-Kirkpatrick model
• Mean field bipartite spin models treated with mechanical techniques

Cited by in corpus (8)

• Phase Diagram of Restricted Boltzmann Machines and Generalised Hopfield Networks with Arbitrary Priors
• Replica Symmetry Breaking in Bipartite Spin Glasses and Neural Networks
• Non-Convex Multi-species Hopfield models
• Neural Networks retrieving Boolean patterns in a sea of Gaussian ones
• Complete integrability of information processing by biochemical reactions
• Hopfield model with planted patterns: a teacher-student self-supervised learning model
• The aggregate path coupling method for the Potts model on bipartite graph
• Modeling Structured Data Learning with Restricted Boltzmann Machines in the Teacher-Student Setting