Energy Spectrum for the System of N Ising Spins with Identical Spin-Spin Coupling K/N - Anatomy of Phase Transition

For the Kittel-Shore-Kac interspin coupling K/N between N Ising spins the ferromagnetic phase transition in specific heat vs. T plot has appeared in literature as a purely mathematical phenomenon, via the exact calculation of the sum of states Z(T) and subsequent differentiations with respect to temperature T. Physical nature of the transition remains in such derivation invisible. As it is expected to be related to the interaction/temperature competition in populating energy levels of the system, in this paper we construct the density of energy states D(E) (or energy spectrum) of such systems, both for the ferromagnetic (K>0) and antiferromagnetic (K<0) coupling between spins. This allows one to see the essence of the difference between these systems as related to the discrete vs. quasi-continuous shape of the spectra at low energy states.