Notes on ferromagnetic diluted P-spin model

TL;DR

This paper introduces an interpolating cavity field technique for the mean field ferromagnetic p-spin model, extending the diluted Curie-Weiss model to higher interactions, analyzing free energy properties, and confirming a first order phase transition through simulations.

Contribution

It develops a novel analytical method for the ferromagnetic p-spin model and extends known results to higher spin interactions with comprehensive analysis.

Findings

The free energy expressions match known models for p=2 and fully connected cases for p>2.

Numerical simulations confirm the presence of a first order phase transition.

Analytical results align well with numerical data and previous research.

Abstract

In this paper we develop the interpolating cavity field technique for the mean field ferromagnetic p-spin. The model we introduce is a natural extension of the diluted Curie-Weiss model to p>2 spin interactions. Several properties of the free energy are analyzed and, in particular, we show that it recovers the expressions already known for p=2 models and for p>2 fully connected models. Further, as the model lacks criticality, we present extensive numerical simulations to evidence the presence of a first order phase transition and deepen the behavior at the transition line. Overall, a good agreement is obtained among analytical results, numerics and previous works.