Influence of Long-Range Interaction on Eigenvalues of Connection Matrix in One-Dimensional Ising Model

Abstract

We analyze a finite one-dimensional Ising system with periodic boundary conditions taking into account an arbitrary long-range interaction. We examine a discrete spectrum of eigenvalues of the spin connection matrix and a spectrum density of a continuous distribution obtained in the limit $$L \to \infty $$ (L is the linear size of the system). We apply our results to particular cases of long-range interactions decreasing with distance.