Eur. Phys. J. Plus (2022) 137: 837
https://doi.org/10.1140/epjp/s13360-022-03052-4

Regular Article

Formation of couples of topological defects in one-dimensional magnetic dipole systems

¹ Faculty of Engineering and Natural Sciences, Bahcesehir University, Ciragan Cad. Osmanpasa Mektebi Sok.Besiktas, 34349, Istanbul, Turkey
² Bahcesehir College Science and Technology, Bahcesehir, 34488, Istanbul, Turkey

^c lutfi.arda@eng.bau.edu.tr

Received: 5 May 2022
Accepted: 8 July 2022
Published online: 20 July 2022

Abstract

In this study, emphasis is placed on the ordering of three-dimensional point dipoles, with continuous degrees of freedom, arranged on a regular ring at low temperatures and a zero external magnetic field, where interactions are long-range. The perfectly ordered state of the system at low temperatures is destroyed with the appearance of north–north (‘NN’-positive) or south-south (‘SS’-negative) point defects. These defects appear above a certain critical temperature $T_c={\epsilon }_f/ln\left(N/2-1\right)$, where ${\epsilon }_f$ is the energy of defect formation at low temperatures, and N is the number of dipoles in the model. On increasing the temperature, the number of defects increases and as a result the system undergoes a continuous topological order–disorder transition, similar to the Kosterlits-Thoulless topological phase transitions found in 2-D systems: in one-dimensional systems, instead of vortex defects, we observe coupled, bounded NN-SS point defects. Based on the Boltzmann statistics, an exact law-temperature solution for the model is obtained which may also be extrapolated to high temperatures.