Vortex screening and the fate of the BKT transition with long-range couplings
cond-mat.stat-mech, cond-mat.quant-gas, hep-th
Submitted: 2026-10-07
Updated: 2026-10-07
Comments: 7+6 pages, 2 figures
License: http://creativecommons.org/licenses/by/4.0/
The gist: The stability of the Berezinskii--Kosterlitz--Thouless phase against long-range interactions remains an open problem.
Terminology
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 about sqrt 7/4-σ as it merges with the Gaussian line.
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