Nucleation-type criticality with infinite number of free-energy minima beyond mean-field theory
Abstract
We study the phase diagram of a three-dimensional Heisenberg model with Dzyaloshinski--Moriya interaction under the presence of Potts-like anisotropy. The phase transition between the winding phase and the ferromagnetically ordered phase exhibits a critical phase transition with anomalous features such as critical exponents consistent with that of a first-order transition while maintaining continuity of physical quantities. Furthermore, at the critical point, we see a growing number of free energy local minima, supporting the picture of infinitely many discontinuous transitions forming criticality. Our numerical result unify de Gennes' theory of nucleation-type transitions and Dzyaloshinskii's calculation of chiral magnets by demonstrating that such anomalous criticality can be realized in microscopic models beyond mean-field.
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BibTeX
@misc{takahashi2026nucleationtype,
title = {{Nucleation-type criticality with infinite number of free-energy minima beyond mean-field theory}},
author = {Jun Takahashi and Yoshihiko Nishikawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26638},
eprint = {2610.26638},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26638},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nucleation-type criticality with infinite number of free-energy minima beyond mean-field theory
AU - Jun Takahashi
AU - Yoshihiko Nishikawa
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26638
UR - https://arxiv.org/abs/2610.26638
AB - We study the phase diagram of a three-dimensional Heisenberg model with Dzyaloshinski--Moriya interaction under the presence of Potts-like anisotropy. The phase transition between the winding phase and the ferromagnetically ordered phase exhibits a critical phase transition with anomalous features such as critical exponents consistent with that of a first-order transition while maintaining continuity of physical quantities. Furthermore, at the critical point, we see a growing number of free energy local minima, supporting the picture of infinitely many discontinuous transitions forming criticality. Our numerical result unify de Gennes' theory of nucleation-type transitions and Dzyaloshinskii's calculation of chiral magnets by demonstrating that such anomalous criticality can be realized in microscopic models beyond mean-field.
ER -