Ferromagnetism in one dimension: Critical Temperature

TL;DR

This paper investigates ferromagnetism in one-dimensional systems by estimating the critical temperature using Binder's method, considering long-range interactions decaying as a power law, and analyzing the transition between different magnetic phases.

Contribution

It introduces a model with power-law decaying interactions to study critical temperature behavior in 1D ferromagnets, highlighting the crossover from mean-field to short-range limits.

Findings

Critical temperature decreases as interaction range shortens.

The model approaches mean-field behavior when interactions are long-range.

Transition between magnetic phases depends on the decay parameter lpha.

Abstract

Ferromagnetism in one dimension is a novel observation which has been reported in a recent work (P. Gambardella et.al., Nature {\bf 416}, 301 (2002)), anisotropies are responsibles in that relevant effect. In the present work, another approach is used to obtain transition between two different magnetic ordering phases. Critical temperature has been estimated by Binder method. Ferromagnetic long range interactions have been included in a special Hamiltonian through a power law that decays at large inter-particle distance $r$ as $r^{-\alpha}$, where $\alpha\geq0$. For the present model, we have found that the trend of the critical temperature vanishes when the range of interactions decreases ($\alpha\to\infty$) and close to mean field approximation when the range of interactions increases ($\alpha\to0$). The crossover between two these limit situations is discussed