Geometrical vs. Fortuin-Kasteleyn clusters in the two-dimensional q-state Potts model

Nuclear Physics B

Volumn 700, Issue 1-3, 2004, Pages 385-406

  Janke, Wolfhard ^a   Schakel, Adriaan M J ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7244229716     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2004.08.030     Document Type: Article

References (47)

1. R.B. Potts Proc. Cambridge Philos. Soc. 48 1952 106
2. C.M. Fortuin P.W. Kasteleyn Physica 57 1972 536
3. F.Y. Wu Rev. Mod. Phys. 54 1982 235
4. D. Stauffer A. Aharony Introduction to Percolation Theory second ed. 1994 Taylor & Francis London
5. R.H. Swendsen J.S. Wang Phys. Rev. Lett. 58 1987 86
6. U. Wolff Phys. Rev. Lett. 62 1989 361
7. R.J. Baxter J. Phys. C 6 1973 L445
8. B. Nienhuis A.N. Berker E.K. Riedel M. Schick Phys. Rev. Lett. 43 1979 737
9. O. Schramm Israel J. Math. 118 2000 221
10. M.P.M. den Nijs J. Phys. A 12 1979 1857
11. M.P.M. den Nijs Phys. Rev. B 27 1983 1674
12. B. Nienhuis J. Phys. A 15 1982 199
13. B. Nienhuis in: C. Domb J.L. Lebowitz (Eds.) Phase Transitions and Critical Phenomena, vol. 11 1987 Academic Press London 1
14. H. Saleur B. Duplantier Phys. Rev. Lett. 58 1987 2325
15. J. Cardy in: C. Domb J.L. Lebowitz (Eds.) Phase Transitions and Critical Phenomena, vol. 11 1987 Academic Press London 55
16. B. Duplantier J. Stat. Phys. 110 2003 691
17. S. Rohde O. Schramm Basic properties of SLE math.PR/0106036 Ann. Math., in press
18. M. Bauer D. Bernard Commun. Math. Phys. 239 2003 493
19. B. Duplantier Conformal fractal geometry and boundary quantum gravity math-ph/0303034
20. A.L. Stella C. Vanderzande Phys. Rev. Lett. 62 1989 1067
21. C. Vanderzande A.L. Stella J. Phys. A 22 1989 L445
22. T. Temesvári L. Herényi J. Phys. A 17 1984 1703
23. A. Coniglio W. Klein J. Phys. A 13 1980 2775
24. B. Duplantier J. Stat. Phys. 49 1987 411
25. H.-M. Erkinger, A new cluster algorithm for the Ising model, Diplomarbeit, Technische Universität Graz, 2000
26. B. Duplantier H. Saleur Phys. Rev. Lett. 61 1988 1521
27. K.K. Murata J. Phys. A 12 1979 81
28. C. Vanderzande J. Phys. A 25 1992 L75 A typo seems to be present in the right hand of Eq. (10) of that paper, giving the fractal dimension of the red bonds of the geometrical clusters. It should read (-4m - 3)/2m(m + 1), where m is related to κ. through Eq. (16). The corresponding entries in Table 1 of that paper should be updated accordingly
29. A.M.J. Schakel Phys. Rev. E 63 2001 026115
30. A.M.J. Schakel J. Low Temp. Phys. 129 2002 323
31. A. Coniglio Phys. Rev. Lett. 62 1989 3054
32. B. Duplantier Phys. Rev. Lett. 84 2000 1363
33. T. Grossman A. Aharony J. Phys. A 19 1986 L745
34. T. Grossman A. Aharony J. Phys. A 20 1987 L1193
35. M. Aizenman B. Duplantier A. Aharony Phys. Rev. Lett. 83 1999 1359
36. J. Asikainen A. Aharony B.B. Mandelbrot E.M. Rauch J.-P. Hovi Eur. Phys. J. B 34 2003 479
37. H.E. Stanley J. Phys. A 10 1977 L211
38. B. Duplantier H. Saleur Phys. Rev. Lett. 63 1989 2536
39. R.P. Feynman Statistical Mechanics 1972 Benjamin Reading
40. H.A. Kramers G.H. Wannier Phys. Rev. 60 1941 252
41. R. Peierls Proc. Cambridge Philos. Soc. 32 1936 477
42. B. Kaufman Phys. Rev. 76 1949 1232
43. A.E. Ferdinand M.E. Fisher Phys. Rev. 185 1969 832
44. W. Janke Monte Carlo simulations of spin systems in: K.H. Hoffmann M. Schreiber (Eds.) Computational Physics: Selected Methods, Simple Exercises, Serious Applications 1996 Springer Berlin 10
45. K. Binder D.W. Heermann Monte Carlo Simulation in Statistical Physics 1997 Springer Berlin
46. J.L. Cambier M. Nauenberg Phys. Rev. B 34 1986 8071
47. V.S. Dotsenko M. Picco P. Windey G. Harris E. Martinec E. Marinari Nucl. Phys. B 448 1995 577