Competing magnetic and spin vestigial orders from continuum field theory
Abstract
We study magnetic systems featuring competing antiferromagnetic and spin-nematic phases, described by dipolar primary and quadrupolar secondary order parameters. While the antiferromagnetic phase breaks time-reversal and spin-rotational symmetries, only spin-rotational symmetry is broken in the nematic phase, which can be understood as a spin-vestigial phase. We develop a classical continuum field theory with independent vector and tensor fields and use mean-field and renormalization group methods to analyze its phases and finite-temperature transitions. We determine the fixed-point structure using an ε expansion about the upper critical dimension of six and track the resulting fixed points to lower dimensions using a perturbative fixed-dimension renormalization group approach. The multicritical fixed point governing the meeting of the antiferromagnetic, nematic, and paramagnetic phases occurs at imaginary coupling throughout the dimensions accessible to our analysis, indicating a first-order transition through the triple point. Away from the triple point, a direct paramagnetic-to-antiferromagnetic transition can be continuous when the tensor mass is sufficiently large, without an intervening vestigial phase. We argue that it is governed by the cubic universality class in d=3 and the Ising universality class in d=2 for three-component order parameters. The theory also supports a two-step transition with an intermediate spin-nematic phase. The paramagnetic-to-nematic transition is governed by the four-state Potts universality class in d=2 and is first order in d=3, while the nematic-to-antiferromagnetic transition is generically expected to be continuous and of Ising type in both dimensions. Our results provide a field-theoretical framework for understanding the finite-temperature transitions observed in the candidate Kitaev material Na2Co2TeO6.
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BibTeX
@misc{francini2026competing,
title = {{Competing magnetic and spin vestigial orders from continuum field theory}},
author = {Niccolò Francini and Lukas Janssen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28620},
eprint = {2609.28620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28620},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Competing magnetic and spin vestigial orders from continuum field theory
AU - Niccolò Francini
AU - Lukas Janssen
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28620
UR - https://arxiv.org/abs/2609.28620
AB - We study magnetic systems featuring competing antiferromagnetic and spin-nematic phases, described by dipolar primary and quadrupolar secondary order parameters. While the antiferromagnetic phase breaks time-reversal and spin-rotational symmetries, only spin-rotational symmetry is broken in the nematic phase, which can be understood as a spin-vestigial phase. We develop a classical continuum field theory with independent vector and tensor fields and use mean-field and renormalization group methods to analyze its phases and finite-temperature transitions. We determine the fixed-point structure using an ε expansion about the upper critical dimension of six and track the resulting fixed points to lower dimensions using a perturbative fixed-dimension renormalization group approach. The multicritical fixed point governing the meeting of the antiferromagnetic, nematic, and paramagnetic phases occurs at imaginary coupling throughout the dimensions accessible to our analysis, indicating a first-order transition through the triple point. Away from the triple point, a direct paramagnetic-to-antiferromagnetic transition can be continuous when the tensor mass is sufficiently large, without an intervening vestigial phase. We argue that it is governed by the cubic universality class in d=3 and the Ising universality class in d=2 for three-component order parameters. The theory also supports a two-step transition with an intermediate spin-nematic phase. The paramagnetic-to-nematic transition is governed by the four-state Potts universality class in d=2 and is first order in d=3, while the nematic-to-antiferromagnetic transition is generically expected to be continuous and of Ising type in both dimensions. Our results provide a field-theoretical framework for understanding the finite-temperature transitions observed in the candidate Kitaev material Na_2Co_2TeO_6.
ER -