A Monte Carlo Study of the Dipolar Universality Class in Three Dimensions

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior and universality class of 3D ferromagnets with dipolar interactions, providing new numerical estimates of critical exponents.

Contribution

Introduces a lattice model and a specialized Monte Carlo algorithm to simulate the dipolar universality class in three dimensions, bridging a gap in computational studies.

Findings

Confirmed a continuous phase transition in the model.

Estimated critical exponents and Binder ratio consistent with theoretical predictions.

Observed emergence of rotation invariance at the critical point.

Abstract

The dipolar universality class describes the phase transition in 3D ferromagnets with strong dipolar interactions, as first discussed by Aharony and Fisher in the 1970s. While this universality class has been studied theoretically using renormalization group methods, as well as experimentally, little is known about it from Monte Carlo simulations. In this paper we aim to bridge this gap. We introduce a lattice model that faithfully implements the transverse constraint on the order parameter. We introduce a Markov Chain Monte Carlo algorithm which involves a combination of local Metropolis updates preserving the constraint, and a global update of the zero mode. We perform simulations on cubic lattices up to volume $48\times 48 \times 48$. We observe a continuous phase transition between the disordered and ordered phases. We obtain estimates of universal quantities such as the main critical exponents and the Binder ratio, and compare them with results from other techniques. We also investigate the emergence of rotation invariance at the critical point.