Exact Solutions of the One-Dimensional, Two-Dimensional, and Three-Dimensional Ising Models

Abstract

According to the traditional solutions, there is no magnetisation in the one-dimensional Ising model in the absence of external magnetic field. It is shown that there is a mistake within them. In them, local order of spins was not taken into account and the partition function and the correlation function were calculated wrongly. In this paper, that mistake is corrected and a new solution is presented. According to it, there is ferromagnetism in that model. Analogously, solutions of the two-dimensional and three-dimensional Ising models are obtained.

Keywords: Nanostructures, Magnetic structure, Magnetic properties, Magnetic materials, Phase transitions