RSS feeds
РусскийEnglish
Issue 4, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2017

 / 

September

←  →

Reviews of topical problems


Berezinskii—Kosterlitz—Thouless transition and two-dimensional melting

, , ,
Institute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation

The main aspects of the theory of phase transitions in two-dimensional degenerate systems (Berezinskii—Kosterlitz—Thouless, or BKT, transitions) are reviewed in detail, including the transition mechanism, the renormalization group as a tool for describing the transition, and how the transition scenario can possibly depend on the core energy of topological defects (in particular, in thin superconducting films). Various melting scenarios in two-dimensional systems are analyzed, and the current status of actual experiments and computer simulations in the field is examined. Whereas in three dimensions melting always occurs as a single first-order transition, in two dimensions, as shown by Halperin, Nelson and Young, melting via two continuous BKT transitions with an intermediate hexatic phase characterized by quasi-long range orientational order is possible. There is also a possibility, however, for a first-order phase transition to occur. Recently, one further melting scenario, different from that occurring in the Berezinskii—Kosterlitz—Thouless—Halperin—Nelson—Young (BKTHNY) theory, has been proposed, according to which a solid can melt in two stages — a continuous BKT type solid-hexatic transition and then a first order hexatic phase—isotropic liquid one. Particular attention is given to the melting scenario as a function of the potential shape and to the random pinning effect on two-dimensional melting. In particular, it is shown that random pinning can alter the melting scenario fundamentally in the case of a first-order transition. Also considered is the melting of systems with potentials having a negative curvature in the repulsion region — potentials that are successfully used in describing the anomalous properties of water in two dimensions.

Fulltext pdf (906 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2017.06.038161
Keywords: two-dimensional systems, Berezinskii—Kosterlitz—Thouless transition, superfluid films, superconducting films, XY model, two-dimensional crystals, topological defects, vortices, dislocations, disclinations, hexatic phase, two-dimensional melting, Berezinskii—Kosterlitz—Thouless—Halperin—Nelson—Young theory, first order transition
PACS: 02.70.Ns, 05.70.Ln, 64.10.+h, 64.60.Ej, 64.70.D− (all)
DOI: 10.3367/UFNe.2017.06.038161
URL: https://ufn.ru/en/articles/2017/9/a/
000417704200001
2-s2.0-85040965639
2017PhyU...60..857R
Citation: Ryzhov V N, Tareyeva E E, Fomin Yu D, Tsiok E N "Berezinskii—Kosterlitz—Thouless transition and two-dimensional melting" Phys. Usp. 60 857–885 (2017)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 15th, May 2017, revised: 23rd, June 2017, 29th, June 2017

Оригинал: Рыжов В Н, Тареева Е Е, Фомин Ю Д, Циок Е Н «Переход Березинского—Костерлица—Таулеса и двумерное плавление» УФН 187 921–951 (2017); DOI: 10.3367/UFNr.2017.06.038161

References (313) Cited by (76) Similar articles (20) ↓

  1. V.N. Ryzhov, E.E. Tareyeva et al “Complex phase diagrams of systems with isotropic potentials: results of computer simulations” 63 417–439 (2020)
  2. B.A. Klumov “Universal structural properties of three-dimensional and two-dimensional melts” 66 288–311 (2023)
  3. V.V. Brazhkin, A.G. Lyapin et al “Where is the supercritical fluid on the phase diagram?” 55 1061–1079 (2012)
  4. B.M. Smirnov “Melting of clusters with pair interaction of atoms” 37 1079–1096 (1994)
  5. V.E. Fortov, A.G. Khrapak et al “Dusty plasmas” 47 447–492 (2004)
  6. V.F. Gantmakher, V.T. Dolgopolov “Superconductor-insulator quantum phase transition” 53 1–49 (2010)
  7. D.K. Belashchenko “Does the embedded atom model have predictive power?” 63 1161–1187 (2020)
  8. R.S. Berry, B.M. Smirnov “Modeling of configurational transitions in atomic systems” 56 973–998 (2013)
  9. I.V. Kukushkin, V.B. Timofeev “Magneto-optics of two-dimensional electron systems in the ultraquantum limit: incompressible quantum liquids and the Wigner crystal” 36 (7) 549–571 (1993)
  10. D.K. Belashchenko “Computer simulation of liquid metals” 56 1176–1216 (2013)
  11. V.V. Prudnikov, P.V. Prudnikov, M.V. Mamonova “Nonequilibrium critical behavior of model statistical systems and methods for the description of its features” 60 762–797 (2017)
  12. M.Yu. Kagan, A.V. Turlapov “BCS—BEC crossover, collective excitations, and hydrodynamics of superfluid quantum fluids and gases” 62 215–248 (2019)
  13. V.F. Khirnyi, A.A. Kozlovskii “Dynamic dissipative mixed states in inhomogeneous type II superconductors” 47 273–288 (2004)
  14. S.M. Stishov “The thermodynamics of melting of simple substances” 17 625–643 (1975)
  15. G.N. Sarkisov “Approximate equations of the theory of liquids in the statistical thermodynamics of classical liquid systems” 42 545–561 (1999)
  16. A.A. Katanin, V.Yu. Irkhin “Magnetic order and spin fluctuations in low-dimensional insulating systems” 50 613–635 (2007)
  17. L.V. Kulik, A.V. Gorbunov et al “Spin excitations in two-dimensional electron gas, their relaxation, photoexcitation and detection methods, and the role of Coulomb correlations” 62 865–891 (2019)
  18. K.V. Larionov, P.B. Sorokin “Investigation of atomically thin films: state of the art” 64 28–47 (2021)
  19. R.S. Berry, B.M. Smirnov “Phase transitions in various kinds of clusters” 52 137–164 (2009)
  20. A.I. Olemskoi, I.V. Koplyk “The theory of spatiotemporal evolution of nonequilibrium thermodynamic systems” 38 1061–1097 (1995)

The list is formed automatically.
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions