The phase transition in the anisotropic Heisenberg model with long range dipolar interactions

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.Comment: Accepted for publication in the Journal of Magnetism and Magnetic Materials. arXiv admin note: substantial text overlap with arXiv:1109.184

Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition

Using the two dimensional $XY-(S(O(3))$ model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless ($BKT$) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the $BKT$ class of universality. We obtain $T_{BKT}$ in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions $\mathfrak{Re}(T) \leq T_{BKT}$ and $\mathfrak{Re}(T) > T_{BKT}$ in the thermodynamic limit show that $\mathfrak{Im}(T)$ goes to zero in the former case and is finite in the last one

Conditions for free magnetic monopoles in nanoscale square arrays of dipolar spin ice

We study a modified frustrated dipolar array recently proposed by M\"{o}ller and Moessner [Phys. Rev. Lett. \textbf{96}, 237202 (2006)], which is based on an array manufactured lithographically by Wang \emph{et al.} [Nature (London) \textbf{439}, 303 (2006)] and consists of introducing a height offset $h$ between islands (dipoles) pointing along the two different lattice directions. The ground-states and excitations are studied as a function of $h$. We have found, in qualitative agreement with the results of M\"{o}ller and Moessner, that the ground-state changes for $h>h_{1}$, where $h_{1}= 0.444a$ ($a$ is the lattice parameter or distance between islands). In addition, the excitations above the ground-state behave like magnetic poles but confined by a string, whose tension decreases as $h$ increases, in such a way that for $h\approx h_1$ its value is around 20 times smaller than that for $h=0$. The system exhibits an anisotropy in the sense that the string tension and magnetic charge depends significantly on the directions in which the monopoles are separated. In turn, the intensity of the magnetic charge abruptly changes when the monopoles are separated along the direction of the longest axis of the islands. Such a gap is attributed to the transition from the anti to the ferromagnetic ground-state when $h=h_1$.Comment: 6 pages, 7 figures. Published versio

Phase transition in the two-dimensional dipolar Planar Rotator model

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)].Comment: 6 pages, 8 figures, Submitted to Journal of Physics: Condensed Matte