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Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class

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arxiv 2405.19411 v4 pith:6M2MFG6W submitted 2024-05-29 hep-th cond-mat.stat-mechcond-mat.str-el

Marten Reehorst , Slava Rychkov , Benoit Sirois , Balt C. van Rees This is my paper · ORCID
classification hep-thcond-mat.stat-mechcond-mat.str-el
keywords bootstrapconformalcriticalfixedmethodsmodelsnumericalpoint
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abstract

We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from perturbative and non-perturbative renormalization group methods have produced mutually incompatible results. We use numerical conformal bootstrap methods to constrain $N_c(d)$ for $3 \leq d < 4$. Our results show that $N_c> 3.78$ for $d = 3$. This favors the scenario that the physically relevant models with $N = 2,3$ in $d=3$ do not have a stable fixed point, indicating a first-order transition. Our result exemplifies how conformal windows can be rigorously constrained with modern numerical bootstrap algorithms.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Redundancy Channels in the Conformal Bootstrap

    hep-th 2025-07 conditional novelty 7.0 of 10

    Redundant operators motivate spectral gaps that block accidental symmetry enhancement, yielding the first bootstrap island for the 3D cubic CFT that excludes the O(3) model.

  2. The tricritical Ising CFT and conformal bootstrap

    hep-th 2025-01 conditional novelty 7.0 of 10

    First conformal-bootstrap islands for the tricritical Ising CFT in d=2.5 and d=2.75, consistent with Padé interpolations between the 3−ε expansion and the exact 2d minimal model.

  3. Bootstrapping 3D Conformal Field Theories with Product Analytic Functionals

    hep-th 2026-08 conditional novelty 6.5 of 10

    A bootstrap method using product analytic functionals gives stronger, faster-converging bounds in three-dimensional conformal field theory, including a new kink near external dimension 4.16.

  4. Bootstrapping the Simplest Deconfined Quantum Critical Point

    hep-th 2025-07 conditional novelty 6.0 of 10

    Conformal bootstrap bounds for U(1)-charged scalars in 3d are saturated by the CP^2 model's large-N and lattice predictions, suggesting the CP^2 deconfined quantum critical point is a conformal field theory.

  5. Physics of 2D magnets and magnetic thin films: Surface structure and surface phase transition, criticality and skyrmions

    cond-mat.stat-mech 2024-12 conditional novelty 1.0 of 10

    A review of surface effects in 2D magnets and ultrathin films, summarizing published results on spin waves, phase transitions, and skyrmions.

  6. Frustrated Spin Systems: History of the Emergence of a Modern Physics

    cond-mat.stat-mech 2024-11 conditional

    This review chronicles the emergence of frustration physics in spin systems and re-presents the author's published results on exact Ising models, fully frustrated lattices, skyrmions, and spin-wave theory.

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