Phase transition in the two-dimensional dipolar Planar Rotator model

TL;DR

This study uses Monte Carlo simulations and finite size scaling to analyze the phase transition in the dipolar XY model, revealing unique critical exponents and behavior distinct from known universality classes.

Contribution

It provides the first detailed Monte Carlo analysis of the dipolar Planar Rotator model considering true long-range interactions with new critical exponents.

Findings

Critical exponents: ν=1.277, β=0.2065, γ=2.218

Critical temperature Tc=1.201

Specific heat appears non-divergent

Abstract

In this work we have used extensive Monte Carlo simulations and finite size scaling theory to study the phase transition in the dipolar Planar Rotator model (dPRM), also known as dipolar XY model. The true long-range character of the dipolar interactions were taken into account by using the Ewald summation technique. Our results for the critical exponents does not fit those from known universality classes. We observed that the specific heat is apparently non-divergent and the critical exponents are $\nu=1.277(2)$, $\beta=0.2065(4)$ and $\gamma=2.218(5)$. The critical temperature was found to be $T_c=1.201(1)$. Our results are clearly distinct from those of a recent Renormalization Group study from Maier and Schwabl [PRB 70, 134430 (2004)] and agrees with the results from a previous study of the anisotropic Heisenberg model with dipolar interactions in a bilayer system using a cut-off in the dipolar interactions [PRB 79, 054404 (2009)].