A Monte Carlo Study of the Dipolar Universality Class in Three Dimensions
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× 48 × 48. We observe a continuous phase transition between the disordered and ordered phases. We obtain estimates of the critical exponent ν and the critical Binder ratio, and compare them with results from other techniques. We also study whether rotational invariance emerges at the critical point, and discuss the influence of the toroidal geometry on this question.
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BibTeX
@misc{matsumoto2026monte,
title = {{A Monte Carlo Study of the Dipolar Universality Class in Three Dimensions}},
author = {Akira Matsumoto and Yu Nakayama and Toshiki Onagi and Slava Rychkov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.11573},
eprint = {2605.11573},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.11573},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Monte Carlo Study of the Dipolar Universality Class in Three Dimensions
AU - Akira Matsumoto
AU - Yu Nakayama
AU - Toshiki Onagi
AU - Slava Rychkov
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2605.11573
UR - https://arxiv.org/abs/2605.11573
AB - 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× 48 × 48. We observe a continuous phase transition between the disordered and ordered phases. We obtain estimates of the critical exponent ν and the critical Binder ratio, and compare them with results from other techniques. We also study whether rotational invariance emerges at the critical point, and discuss the influence of the toroidal geometry on this question.
ER -