Statistical mechanics of the electron-phonon system

Attractive smooth electron-electron interaction generated by phonons in the Fr\"olich Hamiltonian model can be stabilized by the addition of smooth repulsive interaction (like a screened Coulomb repulsion). The thermodynamic limit can be shown to exist in the low densit high temperature regimes. The case of non smoth interactions can also be treated in two-dimensional systems and stability achieved by the addition of a hard core interaction of arbitrarily small radiu