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 on 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 © 2008 John Wiley & Sons, Ltd.