Vortex screening and the fate of the BKT transition with long-range couplings

Abstract

The stability of the Berezinskii--Kosterlitz--Thouless phase against long-range interactions remains an open problem. We address this question in the two-dimensional XY model with couplings decaying as r^−2−σ, by developing a real-space renormalization-group treatment near the Gaussian manifold of quasi-long-range ordered (QLRO) states. We retain the full many-body vortex interaction and show that, at leading order in the fugacity, screening by small vortex--antivortex pairs preserves its Gaussian-average representation without an expansion in the long-range coupling. Including spin waves perturbatively then yields a local stability criterion: a stable QLRO interval exists only for σ>7/4. We also investigate a Wilson--Fisher-like fixed point at finite coupling for σ<7/4, for which the retained flow predicts ν⁻¹∼√(7/4−σ) as it merges with the Gaussian line.

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BibTeX RIS

BibTeX

@misc{giachetti2026vortex,
  title = {{Vortex screening and the fate of the BKT transition with long-range couplings}},
  author = {Guido Giachetti},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10171},
  eprint = {2610.10171},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05829882v1},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Vortex screening and the fate of the BKT transition with long-range couplings
AU  - Guido Giachetti
PY  - 2026
DA  - 2026/10/07
PB  - HAL
DO  - 10.48550/arxiv.2610.10171
UR  - https://hal.science/hal-05829882v1
AB  - The stability of the Berezinskii--Kosterlitz--Thouless phase against long-range interactions remains an open problem. We address this question in the two-dimensional XY model with couplings decaying as r^−2−σ, by developing a real-space renormalization-group treatment near the Gaussian manifold of quasi-long-range ordered (QLRO) states. We retain the full many-body vortex interaction and show that, at leading order in the fugacity, screening by small vortex--antivortex pairs preserves its Gaussian-average representation without an expansion in the long-range coupling. Including spin waves perturbatively then yields a local stability criterion: a stable QLRO interval exists only for σ>7/4. We also investigate a Wilson--Fisher-like fixed point at finite coupling for σ<7/4, for which the retained flow predicts ν^−1∼√(7/4−σ) as it merges with the Gaussian line.
ER  -

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