The Spectral Density of a Spin System Calculated for Solvable Models

The relationship between the spectral density and free energy of a spin system is considered. The analytical expressions allowing for the calculation of the spectral density for solvable models are determined. A linear Ising model is taken for testing the approach. Additionally, the approach is used to analyze the spectral density of a 2D Ising model, a Bethe-lattice model and a mean-field model. Even a small change of the spectral density is shown to be able to radically change the parameters of the system.