System of recursive equations for the partition functions of 1D models
U. A. RozikovInstitute of Mathematics and Information Technologies, 29, Do’rmon Yo’li str., Tashkent, 100125, Uzbekistan
ABI
Abstract
In this note we consider several kind of partition functions of one-dimensional models with nearest — neighbor interactions I n , n ∈ Z and spin values ±1. We derive systems of recursive equations for each kind of such functions. These systems depend on parameters I n , n ∈ Z. Under some conditions on the parameters we describe solutions of the systems of recursive equations.