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.
Highlights
The data of modern studies of the magnetic properties of monoatomic chains [1] [2] raise the question of choosing a model for describing these phenomena and how to solve it
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
We consider a statistical model on a one-dimensional lattice, with nodes numbered by natural numbers 1, N + M, whose partition function has the form
Summary
The data of modern studies of the magnetic properties of monoatomic chains [1] [2] raise the question of choosing a model for describing these phenomena and how to solve it. We study the problems of solving translationally invariant models with a binary interaction of spins located at the nodes of a one-dimensional lattice
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