Phase transition in two-dimensional magnetic systems with dipolar interactions

TL;DR

This study uses Monte Carlo simulations with true long-range dipolar interactions to analyze phase transitions in a 2D magnetic system, revealing unusual critical behavior and emphasizing the importance of accurately modeling long-range anisotropic interactions.

Contribution

It demonstrates the impact of true long-range dipolar interactions on phase transition behavior, challenging previous results that used cut-off approximations.

Findings

Unusual critical exponents consistent with previous models.

Disagreement with Renormalization Group results using cut-off methods.

Long-range anisotropic interactions significantly affect critical behavior.

Abstract

In this work we have used extensive Monte Carlo calculations to study the planar to paramagnetic phase transition in the two-dimensional anisotropic Heisenberg model with dipolar interactions (AHd) considering the true long-range character of the dipolar interactions by means of the Ewald summation. Our results are consistent with an order-disorder phase transition with unusual critical exponents in agreement with our previous results for the Planar Rotator model with dipolar interactions. Nevertheless, our results disagrees with the Renormalization Group results of Maier and Schwabl [PRB, 70, 134430 (2004)] and the results of Rapini et. al. [PRB, 75, 014425 (2007)], where the AHd was studied using a cut-off in the evaluation of the dipolar interactions. We argue that besides the long-range character of dipolar interactions their anisotropic character may have a deeper effect in the system than previously believed. Besides, our results shows that the use of a cut-off radius in the evaluation of dipolar interactions must be avoided when analyzing the critical behavior of magnetic systems, since it may lead to erroneous results.