A multi-temperature kinetic Ising model and the eigenvalues of some perturbed Jacobi matrices

In this paper we analyze the eigenvalues of some perturbed Jacobi matrices. The results contain as particular cases the known spectra of several classes of tridiagonal matrices studied recently. As a motivation, we discuss a three and a four-temperature kinetic Ising model that can be analyzed using some perturbed Jacobi matrices. The analytical results can also be used for the associated reaction–diffusion systems to solve for the particle density.