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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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IMPACT FACTOR 2016: 0.890

CiteScore 2017: 1.41

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2191-0294
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Volume 19, Issue 3-4

Issues

Classical Magnetism and an Integral Formula Involving Modified Bessel Functions

Orion Ciftja
  • Corresponding author
  • Department of Physics, Prairie View A&M University, Prairie View, Texas 77446, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-03-31 | DOI: https://doi.org/10.1515/ijnsns-2017-0193

Abstract

We study an integral expression that is encountered in some classical spin models of magnetism. The idea is to calculate the key integral that represents the building block for the expression of the partition function of these models. The general calculation allows one to have a better look at the internal structure of the quantity of interest which, in turn, may lead to potentially new useful insights. We find out that application of two different approaches to solve the problem in a general-case scenario leads to an interesting integral formula involving modified Bessel functions of the first kind which appears to be new. We performed Monte Carlo simulations to verify the correctness of the integral formula obtained. Additional numerical integration tests lead to the same result as well. The approach under consideration, when generalized, leads to a linear integral equation that might be of interest to numerical studies of classical spin models of magnetism that rely on the well-established transfer-matrix formalism.

Keywords: General Physics; Theory and Modeling; Function Theory and Analysis

PACS: numbers; 01.55.+b; 73.43.Cd; 02.30.-f

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About the article

Received: 2017-08-31

Accepted: 2015-03-15

Published Online: 2018-03-31

Published in Print: 2018-06-26


This research was supported in part by National Science Foundation (NSF) Grants No. DMR-1410350 and DMR-1705084.


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 3-4, Pages 1–6, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2017-0193.

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