# ←→

Reviews of topical problems

# Berezinskii—Kosterlitz—Thouless transition and two-dimensional melting

, , ,
Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, 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 is available at IOP
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/
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

Îðèãèíàë: Ðûæîâ Â Í, Òàðååâà Å Å, Ôîìèí Þ Ä, Öèîê Å Í «Ïåðåõîä Áåðåçèíñêîãî—Êîñòåðëèöà—Òàóëåñà è äâóìåðíîå ïëàâëåíèå» ÓÔÍ 187 921–951 (2017); DOI: 10.3367/UFNr.2017.06.038161

References (313) Cited by (40) ↓ Similar articles (20)

1. Altvater M A, Tilak N et al Nano Lett. 21 6132 (2021)
2. Khali Sh Sh, Chakraborty D, Chaudhuri D Soft Matter 17 3473 (2021)
3. Cardoso D S, Hernandes V F et al Physica A: Statistical Mechanics And Its Applications 566 125628 (2021)
4. Ramírez G Ju P, Cinacchi G Phys. Rev. E 104 (5) (2021)
5. Tsiok E N, Fomin Yu D et al Phys. Rev. E 103 (6) (2021)
6. Altvater M A, Tilak N et al Appl. Phys. Lett. 119 121601 (2021)
7. Khrapak S, Kryuchkov N P et al Phys. Rev. E 103 (5) (2021)
8. Mambretti F, Martinelli M et al Phys. Rev. E 104 (4) (2021)
9. Fomin Yu D Physica A: Statistical Mechanics And Its Applications 565 125519 (2021)
10. Ryzhov V N, Tareyeva E E et al Uspekhi Fizicheskikh Nauk 190 449 (2020)
11. Khrapak S A Phys. Rev. Research 2 (1) (2020)
12. S M M, P O N T et al Journal Of Applied Physics 127 054701 (2020)
13. Komarov K A, Yurchenko S O Soft Matter 16 8155 (2020)
14. Huang P, Schönenberger T et al Nat. Nanotechnol. 15 761 (2020)
15. Smith T  S, Ming F et al Phys. Rev. Lett. 124 (9) (2020)
16. Son L D, Rusakov G M Russ. Metall. 2020 841 (2020)
17. Son L, Sidorov V, Rusakov G Eur. Phys. J. Spec. Top. 229 347 (2020)
18. Tsiok E N, Fomin Yu D, Ryzhov V N Physica A: Statistical Mechanics And Its Applications 550 124521 (2020)
19. Ryzhov V N, Gaiduk E A et al Phys. Part. Nuclei 51 786 (2020)
20. Tsiok E N, Gaiduk E A et al Soft Matter 16 3962 (2020)
21. Mistryukova L A, Kryuchkov N P et al J. Phys.: Conf. Ser. 1348 012097 (2019)
22. Fomin Yu D, Ryzhov V N, Tsiok E N J. Phys.: Condens. Matter 31 315103 (2019)
23. Son L D Russ. Metall. 2019 182 (2019)
24. Komarov K A, Yarkov A V, Yurchenko S O J. Chem. Phys. 151 244103 (2019)
25. Roy I, Dutta S et al Phys. Rev. Lett. 122 (4) (2019)
26. Kryuchkov N P, Mistryukova L A et al Sci Rep 9 (1) (2019)
27. Gaiduk E A, Fomin Yu D et al Molecular Physics 117 2910 (2019)
28. Azizi I, Rabin Y J. Chem. Phys. 150 134502 (2019)
29. Fomin Yu D, Tsiok E N, Ryzhov V N Physica A: Statistical Mechanics And Its Applications 527 121401 (2019)
30. Ryzhov V N, Tareyeva E E Theor Math Phys 200 1053 (2019)
31. Kryuchkov N P, Brazhkin V V, Yurchenko S O J. Phys. Chem. Lett. 10 4470 (2019)
32. Yakovlev E V, Chaudhuri M et al J. Chem. Phys. 151 114502 (2019)
33. Kryuchkov N P, Smallenburg F et al J. Chem. Phys. 150 104903 (2019)
34. Chepurnykh G K, Chernaya V A, Medvedovskaya O G Phys. Solid State 60 1712 (2018)
35. Kryuchkov N P, Ivlev A V, Yurchenko S O Soft Matter 14 9720 (2018)
36. Khrapak S A, Kryuchkov N P et al The Journal Of Chemical Physics 149 134114 (2018)
37. Fomin Yu D, Gaiduk E A et al Molecular Physics 116 3258 (2018)
38. Kryuchkov N P, Yurchenko S O et al Soft Matter 14 2152 (2018)
39. Baeva E M, Sidorova M V et al Phys. Rev. Applied 10 (6) (2018)
40. Digregorio P, Levis D et al Phys. Rev. Lett. 121 (9) (2018)

 © 1918–2021 Uspekhi Fizicheskikh Nauk Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions