Critical behaviour of random-bond Potts models: A transfer matrix study

Nuclear Physics B

Volumn 515, Issue 3, 1998, Pages 701-742

  Jacobsen, Jesper Lykke ^a,b,c   Cardy, John ^a,d  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b AARHUS UNIVERSITY   (Denmark)

^c SOMERVILLE COLLEGE   (United Kingdom)

^d ALL SOULS COLLEGE   (United Kingdom)

Author keywords

Conformal field theory; First order phase transitions; Lyapunov spectra; Potts models; Quenched bond randomness; Transfer matrices

Indexed keywords

EID: 0032489693     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0550-3213(98)00024-8     Document Type: Article

References (63)

1. [1] A.B. Harris, J. Phys. C 7 ( 1974) 1671.
2. [2] A. Aharony, Phys. Rev. B 18 (1978) 3318.
3. [3] Y. Imry and S.-K. Ma, Phys. Rev. Lett. 35 (1975) 1399.
4. [4] Y. Imry and M. Wortis, Phys. Rev. B 19 (1979) 3581.
5. [5] K. Hui and A.N. Barker, Phys. Rev. Lett. 62 (1989) 2507; 63 (1989) 2433 (E).
6. [5] K. Hui and A.N. Barker, Phys. Rev. Lett. 62 (1989) 2507; 63 (1989) 2433 (E).
7. [6] M. Aizenman and J. Wehr, Phys. Rev. Lett. 62 (1989) 2503.
8. [7] J. Cardy, J. Phys. A 29 (1996) 1897.
9. [8] J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge Univ. Press, Cambridge, 1996).
10. [9] P. Pujol, Europhys. Lett. 35 (1996) 283.
11. [10] R.J. Baxter, J. Phys. C 6 (1973) L445.
12. [11] S. Chen, A.M. Ferrenberg and D.P. Landau, Phys. Rev. E 52 (1995) 1377.
13. [12] S. Wiseman and E. Domany, Phys. Rev. E 51 (1995) 3074.
14. [13] M. Kardar, A.L. Stella, G. Sartoni and B. Derrida, Phys. Rev. E 52 (1995) R1269.
15. [14] A.W. W. Ludwig and J.L. Cardy, Nucl. Phys. B 285 [FS19] (1987) 687.
16. [15] A.W.W. Ludwig, Nucl. Phys. B 285 (1987) 97.
17. [16] A.W.W. Ludwig, Nucl. Phys. B 330 ( 1990) 639.
18. [17] VI. Dotsenko, M. Picco and P. Pujol, Nucl. Phys. B 455 (1995) 701.
19. [18] H.W. J. Blöte and M.P. Nightingale, Physica A 112 (1982) 405.
20. [19] J.T. Chayes, L. Chayes, D.S. Fisher and T. Spencer, Phys. Rev. Lett. 57 (1986) 2999.
21. [20] J.T. Chayes, L. Chayes, D.S. Fisher and T. Spencer, Commun. Math. Phys. 120 (1989) 501.
22. [21] M.P. Nightingale, Physica A 83 (1976) 561.
23. [22] Vi. Dotsenko. VI. Dotsenko, M. Picco and P. Pujol. Europhys. Lett. 32 (1996) 425.
24. [23] J. Cardy and J.L. Jacobsen, Phys. Rev. Lett. 79 (1997) 4063.
25. [24] F. Pázmándi, R.T. Scalettar and GT Zimányi, Phys. Rev. Lett. 79 (1997) 5130.
26. [25] R.B. Potts. Proc. Cambr. Philos. Soc. 48 (1952) 106.
27. [26] F.Y. Wu, Rev. Mod. Phys. 54 (1982) 235.
28. [27] W. Kinzel and E. Domany, Phys. Rev. B 23 (1981) 3421.
29. [28] J.L. Cardy, J. Phys. A 16 (1983) L355.
30. [29] H.W. Blöte, J.L. Cardy and M.P. Nightingale, Phys. Rev. Lett. 56 (1986) 742;
31. I. Affleck, Phys. Rev. Lett. 56 (1986) 746.
32. [30] H. Furstenberg, Trans. Am. Math. Soc. 68 (1963) 377.
33. [31] G. Benettin, L. Galgani, A. Giorgilli and J.-M. Strelcyn, Meccanica 15 (1980) 9.
34. [32] T. Bhattacharya, R. Lacaze and A. Morel, J. Phys. I France 7 (1997) 81.
35. [33] A.J. Bray and M.A. Moore, J. Phys C 18 (1985) L927.
36. [34] D. Slauffer, Z. Phys. B 22 (1975) 161.
37. [35] J.L. Cardy (ed.), Finite-Size Scaling (North-Holland, Amsterdam, 1988).
38. [36] P.W. Kasteleyn and C.M. Fortuin, J. Phys. Soc. Jap. 46 (suppl.) (1969) 11.
39. [37] H.W. J. Blöte and B. Nienhuis, J. Phys. A 22 (1989) 1415.
40. [38] F.Y. Wu, Phys. Lett. A 228 (1997) 43.
41. [39] J.L. Jacobsen, Phys. Lett. A 233 (1997) 489.
42. [40] F.Y. Wu and H.Y. Huang, Phys. Rev Lett. 79 (1997) 4954.
43. [41] E. Buffenoir and S. Wallon, J. Phys. A 26 (1993) 3045.
44. [42] S.L. A. de Queiroz, Phys. Rev. E 51 (1995) 1030.
45. [43] J.L. Cardy, in Phase Transitions and Critical Phenomena Vol. 11, ed. C. Domb and J.L. Lebowitz (Academic Press, London, 1987).
46. [44] F.D. A. Aarao Reis, S.L. A. de Queiroz and R. R. dos Santos, Phys. Rev. B 56 (1997) 6013.
47. [45] J.L. Cardy, J. Phys. A 19 (1986) L1093.
48. [46] A.B. Zamolodchikov, Pis'ma Zh. Eksp. Teor. Fiz. 43 (1986) 565. [JETP Lett. 43 (1986) 730.]
49. [46] A.B. Zamolodchikov, Pis'ma Zh. Eksp. Teor. Fiz. 43 (1986) 565. [JETP Lett. 43 (1986) 730.]
50. [47] M. Picco, Phys. Rev. Lett. 79 (1997) 2998.
51. [48] VI.S. Dotsenko and V.A. Fateev, Nucl. Phys. B 240 (1984) 312.
52. [49] B. Derrida, Phys. Rep. 103 (1984) 29.
53. [50] Section 12.5.3 in Ledermann (ed.), Handbook of Applicable Mathematics, Vol. 2: Probability (Wiley, London, 1980).
54. [51] M. Picco, Phys. Rev. B 54 (1996) 14930.
55. [52] M. Picco, private communication.
56. [53] J.L. Cardy, Nucl. Phys. B 270 [FS16] (1986) 186; 366 (1991) 403.
57. [53] J.L. Cardy, Nucl. Phys. B 270 [FS16] (1986) 186; 366 (1991) 403.
58. [54] J.L. Jacobsen, in preparation.
59. [55] W. Janke and R. Villanova, Phys. Lett. A 209 (1995) 179; Nucl. Phys. B (Proc. Suppl.) 47 (1996) 641.
60. [55] W. Janke and R. Villanova, Phys. Lett. A 209 (1995) 179; Nucl. Phys. B (Proc. Suppl.) 47 (1996) 641.
61. [56] A. Okabe, B. Boots and K. Sugihara, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams (Wiley, London, 1992).
62. [57] C.F. Baillie, W. Janke and D.A. Johnston, Phys. Lett. B 388 (1996) 14.
63. [58] W.H. Press et al., Numerical Recipes in C, 2nd Ed. (Cambridge University Press, Cambridge, 1992).