Notes on ferromagnetic p-spin and REM

In this paper we apply some of the recent mathematical techniques (mainly based on interpolation) developed in the spin glass theory to the ferromagnetic p-spin model. We introduce two Hamiltonians and derive their thermodynamics. This is a second step toward an alternative and rigorous formulation of the statistical mechanics of simple systems oil lattice. A first step has been performed in J. Stat. Phys. (2007; arXiv:0712.1344) where the techniques have been tested on the two-body Ising model. For completeness the adaptation of the well-known random energy model to the context of the ferromagnetism is presented. At the end a discussion on the extension of these techniques to Gaussian-disordered p-spin models is also briefly Outlined. Copyright (C) 2008 John Wiley & Sons, Ltd.