Difference-Equation Solutions for the Linear Ising Model and Nearest-Neighbor Fluid

Abstract

The one-dimensional nearest-neighbor Ising model, in the presence of a uniform external magnetic field, is solved using a difference equation technique. The approach involves neither combinatorial analyses nor matrix methods, and can be understood with a minimal knowledge of difference equations. The cases with periodic boundary conditions and with no boundary constraints are treated with equal ease. Similarly, the one-dimensional nearest-neighbor fluid is solved with the aid of difference equation techniques. Some difference-equation theory and the conventional matrix Ising model solutions are outlined in appendixes.