Eur. Phys. J. B (2017) 90: 133
https://doi.org/10.1140/epjb/e2017-80070-3

Regular Article

Langevin dynamics simulation of a one-dimensional linear spin chain with long-range interactions

¹ LEPM, Faculté de physique, Université des Sciences et de la Technologie d’Oran Mohamed Boudiaf, USTO-MB, BP 1505, EL M'naouer, 31000 Oran, Algeria
² Faculty of Physics, Alexandru Ioan Cuza University, 700506 Iasi, Roumania

^a e-mail: amoncef@live.fr , moncef.ati@univ-usto.dz

Received: 31 January 2017
Received in final form: 20 May 2017
Published online: 12 July 2017

Abstract

In this paper we study the critical behavior of a simple one-dimensional rotor spin in the form of a linear chain with long-range interactions, using the mean field Langevin dynamics approach and in the presence of fluctuations added by a heat bath. We have computed the specific heat, the magnetic susceptibility, the Binder fourth-order cumulant, and the magnetization, and then we have calculated the critical exponents using finite-size scaling. In addition, we provide a relation between the thermal bath temperature and the temperature of the system. Our results confirm the existence of a second-order critical temperature in the one-dimensional chain of spins with long-range interaction.