We present some calculations for the thermodynamic behavior of mean-field ferromagnetic p-spin interaction models in the presence of quenched random fields. For both Ising and spherical spin variables, we use the law of large numbers, without recourse to the replica trick, to obtain a...

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p=−J2/J1, where J10 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J2<0 is associated with competing antiferromagnetic interactions between second neighbours along m≤d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0 space, with a Lifshitz point at p=1/4, for d>2, and closed-form...</0>