The Spectral Density of a Spin System Calculated for Solvable Models

TL;DR

This paper develops analytical methods to calculate the spectral density of solvable spin models, demonstrating their application to various models and highlighting the impact of spectral density changes on system parameters.

Contribution

It introduces a new analytical approach for calculating spectral densities in solvable spin models and applies it to multiple models, including 2D Ising and Bethe-lattice.

Findings

Analytical expressions for spectral density are derived.

Small spectral density changes can significantly alter system parameters.

The approach is validated on linear and 2D Ising models.

Abstract

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.