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 behaviour at the transition line. Overall, a good agreement is obtained among analytical results, numerics and previous works.
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