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

I. A. Stepanov. Exact Solutions of the One-Dimensional, Two-Dimensional, and Three-Dimensional Ising Models. – Nano Science & Nano Technology: An Indian Journal. 2012. Vol 6. No 3. 118 - 122

5 Pages Posted: 13 Dec 2017

See all articles by Igor Stepanov

Igor Stepanov

Liepaja University - Institute of Science and Innovative Technologies

Date Written: 2012

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

Suggested Citation

Stepanov, Igor, Exact Solutions of the One-Dimensional, Two-Dimensional, and Three-Dimensional Ising Models (2012). I. A. Stepanov. Exact Solutions of the One-Dimensional, Two-Dimensional, and Three-Dimensional Ising Models. – Nano Science & Nano Technology: An Indian Journal. 2012. Vol 6. No 3. 118 - 122, Available at SSRN: https://ssrn.com/abstract=3076041

Igor Stepanov (Contact Author)

Liepaja University - Institute of Science and Innovative Technologies ( email )

Liela 14
Liepaja, LV-3401
Latvia

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