RSS feeds
РусскийEnglish
Issue 10, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1995

 / 

June

←  →

Reviews of topical problems


Fractals, topological defects, and confinement in lattice gauge theories


Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

Topological defects — monopoles, vortices, and strings — are discussed. It is shown that these objects form clusters with a nonintegral dimension, i.e., they are fractals. The fractal dimension reflects the physical properties of a system. In particular, studies of monopole current clusters in U(1) and SU(2) lattice gauge theories make it possible to identify the confinement mechanism. In the confinement phase the current lines of a magnetic monopole form a percolating cluster and these lines are so dense that their dimension exceeds unity, whereas in the deconfinement phase their dimension is trivial: it is equal to unity. It is also shown that the string tension is proportional to the dimension of extended monopole currents. This is in agreement with a confinement model based on the condensation of magnetic monopoles into a superconducting phase. A string between a quark and an antiquark is then analogous to an Abrikosov vortex in a superconductor. An account is given of the application of the theory of fractals in the problem of gauge fixing in lattice gauge theories. It is also demonstrated that, in SU(2) gluodynamics, domains of the deconfinement phase have a nonintegral dimension near a phase transition point. Apart from monopoles, the review deals also with the properties of vortex and string clusters in three-dimensional and four-dimensional XY models. The corresponding physical objects are vortices in liquid helium and ’global cosmic strings’.

Fulltext pdf (1013 KB)
Fulltext is also available at DOI: 10.1070/PU1995v038n06ABEH000090
PACS: 11.15.Ha, 14.80.Hv, 74.20.De, 64.40.-w (all)
DOI: 10.1070/PU1995v038n06ABEH000090
URL: https://ufn.ru/en/articles/1995/6/b/
A1995RL93800002
Citation: Polikarpov M I "Fractals, topological defects, and confinement in lattice gauge theories" Phys. Usp. 38 591–607 (1995)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Поликарпов М И «Фракталы, топологические дефекты и невылетание в решеточных калибровочных теориях» УФН 165 627–644 (1995); DOI: 10.3367/UFNr.0165.199506b.0627

References (79) ↓ Cited by (14) Similar articles (20)

  1. Mandelbrot B B The Fractal Geometry Of Nature (San Francisco: W H Freeman, 1982)
  2. Paladin G, Vulpiani A Phys. Rep. 156 147 (1987)
  3. Yi-Cheng Zhang, Serva M, Polikarpov M J. Stat. Phys. 58 849 (1990)
  4. Gross D J, Wilczek F Phys. Rev. Lett. 30 1343 (1973)
  5. Politzer H D Phys. Rev. Lett. 30 1346 (1973)
  6. Weinberg S Phys. Rev. Lett. 31 494 (1973)
  7. Bali G S, Schilling K, Schlichter C Preprint CERN-TH.7413/94 (Geneva: Cern, 1994)
  8. ’t Hooft G High Energy Physics Ed. (M Zichichi) (Bologna: Editrice Compositori, 1976)
  9. Mandelstam S Phys. Rev. C 23 245 (1976)
  10. Abrikosov A A Zh. Eksp. Teor. Fiz. 32 1442 (1957); Abrikosov A A Sov. Phys. JETP 5 1174 (1957)
  11. Wiese U-J, Polikarpov M I Pis’ma Zh. Eksp. Teor. Fiz. 51 296 (1990); Wiese U-J, Polikarpov M I JETP Lett. 51 336 (1990)
  12. Polikarpov M I Phys. Lett. B 236 61 (1990)
  13. Engels J, Karsch F, Satz H, Montvay I Nucl. Phys. B [FS5] 545 (1982)
  14. Kuti J, Polonyi J, Szlachanyi K Phys. Lett. B 98 199 (1981)
  15. Polyakov A M Phys. Lett. B 72 477 (1978)
  16. Domb C J. Phys. A 9 L17 (1976)
  17. Binder K Ann. Phys. 98 390 (1976)
  18. Cambier J L, Nauenberg M Proceedings of Sixth Trieste International Symposium on Fractals in Physics (ICTP ’85) Trieste (1985) Eds (L Pietronero, E Tosatti) (Amsterdam: North-Holland, 1986)
  19. Wilson K G Phys. Rev. D 10 2445 (1974)
  20. Polyakov A M Gauge Fields And Strings (New York: Harwood, 1987)
  21. Banks T, Myerson R, Kogut J Nucl. Phys. B 129 493 (1977)
  22. Cardy J L Nucl. Phys. B 170; Cardy J L Nucl. Phys. B [FS1] 369 (1980)
  23. DeGrand T A, Toussaint D Phys. Rev. D 22 2478 (1980)
  24. Kronfeld A S, Schierholz G, Wiese U-J Nucl. Phys. B 293 461 (1987)
  25. Kronfeld A S, Laursen M L, Schierholz G, Wiese U-J Phys. Lett. B 198 516 (1987)
  26. Polley L, Polikarpov M I, Wiese U-J Phys. Lett. B 253 212 (1991)
  27. Ivanenko T L, Polikarpov M I, Pochinskii A V Pis’ma Zh. Eksp. Teor. Fiz. 53 517 (1991); Ivanenko T L, Polikarpov M I, Pochinskii A V JETP Lett. 53 543 (1991)
  28. Ivanenko T L, Pochinsky A V, Polikarpov M I Phys. Lett. B 302 458 (1993)
  29. Essam J W Phase Transitions And Critical Phenomena Vol. 2 Eds (C Domb, M S Green) (New York: Academic Press, 1972)
  30. Grimmett G Percolation (Berlin: Springer, 1989)
  31. ’t Hooft G Nucl. Phys. B [FS3] 455 (1981)
  32. Suzuki T Proceedings of the International Symposium on Lattice Field Theory (Lattice ’92) (Amsterdam, 1992); Suzuki T Nucl. Phys. B (Proc. Suppl.) 30 176 (1993)
  33. Suzuki T, Yotsuyanagi I Phys. Rev. D 42 4257 (1990)
  34. Bornyakov V G, Ilgenfritz E-M, Laursen M L, et al. Phys. Lett. B 261 116 (1991)
  35. Singh V, Browne D, Haymaker R Phys. Lett. B 306 115 (1993)
  36. Shiba H, Suzuki T Preprint 94-07 (Kanazawa, Japan: Kanazawa University, 1994)
  37. Stack J D, Neiman S D, Wensley R J Preprint ILL-(TH)-94-14 (Urbana-Champaign, IL: Dept. of Physics, Illinois University, 1994)
  38. Shiba H, Suzuki T Preprint 94-12 (Kanazawa, Japan: Kanazawa University, 1994)
  39. Ivanenko T L, Polikarpov M I, Pochinsky A V Phys. Lett. B 252 631 (1990)
  40. Kitahara S, Matsubara Y, Suzuki T Preprint 94-24 (Kanazawa, Japan: Kanazawa University, 1994)
  41. Kanaya K, Satz H Phys. Rev. D 34 3193 (1986)
  42. Berg B Phys. Lett. B 104 475 (1981)
  43. Iwasaki Y, Yoshie T Phys. Lett. B 127 197 (1983)
  44. Teper M Phys. Lett. B 162 357 (1985)
  45. Ilgenfritz E M, Laursen M L, Muller-Preussker M, et al. Nucl. Phys. B 268 693 (1986)
  46. Campostrini M, Di Giacomo A, Maggiore M, et al. Phys. Lett. B 225 403 (1989)
  47. Polikarpov M I, Veselov A I Nucl. Phys. B 297 34 (1988)
  48. Chernodub M N, Polikarpov M I, Veselov A I Phys. Lett. B 342 303 (1995)
  49. Chernodub M N, Polikarpov M I, Zubkov M A Proceedings of International Symposium on Lattice Field Theory (Lattice ’93) (Dallas, TX, 1993); Chernodub M N, Polikarpov M I, Zubkov M A Nucl. Phys. B (Proc. Suppl.) 34 256 (1994)
  50. Polikarpov M I, Chernodub M N Pis’ma Zh. Eksp. Teor. Fiz. 59 439 (1994); Polikarpov M I, Chernodub M N JETP Lett. 59 459 (1994)
  51. Smit J, van der Sijs A Nucl. Phys. B 355 603 (1991)
  52. ’t Hooft G Nucl. Phys. B 79 276 (1974)
  53. Polyakov A M Pis’ma Zh. Eksp. Teor. Fiz. 20 430 (1974); Polyakov A M JETP Lett. 20 194 (1974)
  54. Bogomol’nyi E B Ya D. Fiz. 24 861 (1976); Bogomol’nyi E B Sov. J. Nucl. Phys. 24 449 (1976)
  55. Prasad M K, Sommerfield C M Phys. Rev. Lett. 35 760 (1975)
  56. Polikarpov M I, Yee K Phys. Lett. B 333 452 (1994)
  57. Polikarpov M I, Yee K, Zubkov M A Phys. Rev. D 48 3377 (1993)
  58. Vilenkin A Phys. Rep. 121 263 (1985)
  59. Ivanenko T L, Polikarpov M I Preprint ITEP-49 (Moscow: Institute of Theoretical and Experimental Physics, 1991)
  60. Bukenov A K, Wiese U-J, Polikarpov M I, Pochinskii A V Ya D. Fiz. 56 214 (1993); Bukenov A K, Wiese U-J, Polikarpov M I, Pochinskii A V Phys. At. Nucl. 56 122 (1993)
  61. Berezinskii V L Zh. Eksp. Teor. Fiz. 59 907 (1970); Berezinskii V L Sov. Phys. JETP 32 493 (1971)
  62. Kosterlitz J M, Thouless D J J. Phys. C 6 1181 (1973)
  63. Onsager L Nuovo Cimento 6 279 (1949)
  64. Feynman R P Prog. Low Temp. Phys. 1 17 (1955)
  65. Williams G A Phys. Rev. Lett. 59 1926 (1987); Williams G A Erratum 61 1142 (1988)
  66. Shenoy S R Preprint (Karlsruhe, Germany: Universitat Karlsruhe, 1989)
  67. Pochinsky A V, Polikarpov M I, Yurchenko B N Phys. Lett. A 154 194 (1991)
  68. Frohlich J, Marchetti P A Europhys. Lett. 2 933 (1986)
  69. Frohlich J, Marchetti P A Commun. Math. Phys. 112 343 (1987)
  70. Polikarpov M I, Wiese U-J Preprint HLRZ 90-78 (Julich, Germany: Hochstleistungsrechenzentrum, KFA, 1990)
  71. Polikarpov M I, Wiese U-J, Zubkov M A Phys. Lett. B 309 133 (1993)
  72. Dirac P A M Can. J. Phys. 33 650 (1955)
  73. Creutz M Quarks, Gluons And Lattices (Cambridge: Cambridge University Press, 1985)
  74. Makeenko Yu M Usp. Fiz. Nauk 143 161 (1984); Makeenko Yu M Sov. Phys. Usp. 27 401 (1984)
  75. Patrascioiu A, Seiler E, Stamatescu I O Phys. Lett. B 107 364 (1984)
  76. Seiler E, Stamatescu I O, Zwanziger D Nucl. Phys. B 239 177 (1984)
  77. Polyakov A M Phys. Lett. B 59 79 (1975)
  78. Makeenko Yu M, Polikarpov M I Nucl. Phys. B 205; Makeenko Yu M, Polikarpov M I Nucl. Phys. B Vol. [FS5] (1982) p. 386
  79. Metropolis N, Ulam S J. Am. Stat. Assoc. 247 335 (1949)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions