Collective excitations in the anharmonic crystal

We consider a lattice model of an anharmonic crystal and compute the isothermal (χT) and adiabatics (χS) susceptibilities for the lattice displacement below Tc. A detailed analysis is given in terms of the dimension of the lattice and a decay parameter of the harmonic force. It turns out that there is a phase-space region for which 0 < χT/χS < 1, indicating breaking of ergodicity, and a region for which χT is finite, indicating the presence of a plasmon frequency due to the anharmonicity.