TITLE:
On the Solution of One-Dimensional Ising Models
AUTHORS:
Yu. N. Kharchenko
KEYWORDS:
Ising Model, Transfer Matrix, Statistical Sum, Free Energy, Singular Curves, Phase Transitions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.5,
May
16,
2018
ABSTRACT: In this paper it is shown that the thermodynamic limit of the partition function of the statistical models under consideration on a one-dimensional lattice with an arbitrary finite number of interacting neighbors is expressed in terms of the principal eigenvalue of a matrix of finite size. The high sparseness of these matrices for any number of interactions makes it possible to perform an effective numerical analysis of the macro characteristics of these models.