Physics of phase transitions in two dimensions: Berezinskii—Kosterlitz—Thouless and beyond

V.N. Ryzhov^†, V.V. Brazhkin^‡, E.E. Tareyeva^§, Yu.D. Fomin^*, E.N. Tsiok^#
Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation

This review is based on the authors' report at the Scientific Session of the Physical Sciences Division of the Russian Academy of Sciences (RAS). The review discusses the Berezinskii—Kosterlitz—Thouless (BKT) transition in two-dimensional systems with continuous symmetry, including the transition in two-dimensional magnetic systems (X—Y-model), the transition to the superfluid state in ⁴He thin films, and the superconducting transition in thin films. Scenarios of two-dimensional melting in various systems are considered, including soft matter, vortex lattices in superconducting films, and skyrmion lattices. Particular attention is paid to deviations from the standard BKT scenario for various systems depending on the parameters characterizing the system: the type of potential, which is especially important for two-dimensional melting, and the energy of the core of a topological defect.

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Keywords: two-dimensional systems, Berezinskii—Kosterlitz—Thouless transition, superfluid films, superconducting films, X—Y-model, two-dimensional crystals, topological defects, vortices, dislocations, disclinations, hexatic phase, two-dimensional melting, Berezinskii—Kosterlitz—Thouless—Halperin—Nelson—Young theory, first order transition, Bernard—Krauth scenario
PACS: 61.20.Gy, 61.20.Ne, 64.60.Kw (all)
DOI: 10.3367/UFNe.2025.04.040000
URL: https://ufn.ru/en/articles/2026/5/f/
Citation: Ryzhov V N, Brazhkin V V, Tareyeva E E, Fomin Yu D, Tsiok E N "Physics of phase transitions in two dimensions: Berezinskii—Kosterlitz—Thouless and beyond" Phys. Usp. 69 501–523 (2026)

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Received: 18th, July 2025, accepted: 23rd, April 2025

Оригинал: Рыжов В Н, Бражкин В В, Тареева Е Е, Фомин Ю Д, Циок Е Н «Физика фазовых переходов в двух измерениях: за пределами Березинского—Костерлица—Таулеса» УФН 196 537–561 (2026); DOI: 10.3367/UFNr.2025.04.040000

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