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. © 2011 Polish Scientific Publishers.
Notes on ferromagnetic diluted p-spin model / Agliari, Elena; Barra, Adriano; Camboni, Federico. - In: REPORTS ON MATHEMATICAL PHYSICS. - ISSN 0034-4877. - ELETTRONICO. - 68:1(2011), pp. 1-22. [10.1016/s0034-4877(11)60024-4]
Notes on ferromagnetic diluted p-spin model
AGLIARI, ELENA;BARRA, ADRIANO;
2011
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. © 2011 Polish Scientific Publishers.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
