Comparative study of the critical behavior in one-dimensional random and aperiodic environments

European Physical Journal B

Volumn 5, Issue 3, 1998, Pages 613-625

  Igloi F ^a,d,e   Karevski, D ^b   Rieger, H ^c,d  

^a WIGNER RESEARCH CENTRE FOR PHYSICS   (Hungary)

^b INSTITUT JEAN LAMOUR   (France)

^c UNIVERSITY OF COLOGNE   (Germany)

^d FORSCHUNGSZENTRUM JÜLICH   (Germany)

^e UNIVERSITY OF SZEGED   (Hungary)

Author keywords

05.50.+q Lattice theory and statistics; Ising problems; 64.60.Ak Renormalization group, fractal, and percolation studies of phase transitions; 68.35.Rh Phase transitions and critical phenomena

Indexed keywords

MATHEMATICAL MODELS; PHASE TRANSITIONS; RANDOM PROCESSES;

APERIODIC SYSTEMS; ISING PROBLEMS; LATTICE THEORY;

QUANTUM THEORY;

EID: 0032292147     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510050486     Document Type: Article

References (52)

1. Ya.G. Sinai, Theor. Probab. Appl. 27, 247 (1982); for a review on random walks in disordered media see: J.P. Bouchaud, A. Georges, Phys. Rep. 195, 127 (1990).
2. Ya.G. Sinai, Theor. Probab. Appl. 27, 247 (1982); for a review on random walks in disordered media see: J.P. Bouchaud, A. Georges, Phys. Rep. 195, 127 (1990).
3. F. Iglói, H. Rieger, Phys. Rev. B 57, 11404 (1998).
4. H. Rieger, F. Iglói, Europhys. Lett. 39, 135 (1997).
5. R.B. Griffiths, Phys. Rev. Lett. 23, 17 (1969).
6. B. McCoy, Phys. Rev. Lett. 23, 383 (1969).
7. F. Iglói, D. Karevski, H. Rieger, Eur. Phys. J. B 1, 513 (1998).
8. D.S. Fisher, Phys. Rev. Lett. 69, 534 (1992); Phys. Rev. B 51, 6411 (1995).
9. D.S. Fisher, Phys. Rev. Lett. 69, 534 (1992); Phys. Rev. B 51, 6411 (1995).
10. R.H. McKenzie, Phys. Rev. Lett. 77, 4804 (1996).
11. A.P. Young, H. Rieger, Phys. Rev. B 53, 8486 (1996).
12. F. Iglói, H. Rieger, Phys. Rev. Lett. 78, 2473 (1997).
13. A.P. Young, Phys. Rev. B 56, 11691 (1997).
14. See H. Rieger, A.P. Young, in Complex Behavior of Glassy Systems, Lecture Notes in Physics, edited by M. Rubi, C. Perez-Vicente (Springer-Verlag, Heidelberg, 1997) 492, p. 256, for a review on the Ising quantum spin glass in a transverse field.
15. S. Sachdev, T. Senthil, Phys. Rev. Lett. 77, 5292 (1996).
16. H. Rieger, N. Kawashima, Phys. Rev. Lett. (submitted); C. Pich, A.P. Young, Phys. Rev. Lett. (submitted); T. Ikegami, S. Miyashita, H. Rieger, J. Phys. Soc. Jpn (in press).
17. H. Rieger, N. Kawashima, Phys. Rev. Lett. (submitted); C. Pich, A.P. Young, Phys. Rev. Lett. (submitted); T. Ikegami, S. Miyashita, H. Rieger, J. Phys. Soc. Jpn (in press).
18. H. Rieger, N. Kawashima, Phys. Rev. Lett. (submitted); C. Pich, A.P. Young, Phys. Rev. Lett. (submitted); T. Ikegami, S. Miyashita, H. Rieger, J. Phys. Soc. Jpn (in press).
19. B.M. McCoy, T.T. Wu, Phys. Rev. 162, 436 (1967).
20. B.M. McCoy, T.T. Wu, Phys. Rev. 176, 631 (1968); 188, 982 (1969); B.M. McCoy, Phys. Rev. 188, 1014 (1969).
21. B.M. McCoy, T.T. Wu, Phys. Rev. 176, 631 (1968); 188, 982 (1969); B.M. McCoy, Phys. Rev. 188, 1014 (1969).
22. B.M. McCoy, T.T. Wu, Phys. Rev. 176, 631 (1968); 188, 982 (1969); B.M. McCoy, Phys. Rev. 188, 1014 (1969).
23. P. Hoever, W.F. Wolff, J. Zittartz, Z. Phys. B 41, 43 (1981); W.F. Wolff, P. Hoever, J. Zittartz, Z. Phys. B 42, 259 (1981); P. Hoever, J. Zittartz, Z. Phys. B 44, 129 (1981).
24. P. Hoever, W.F. Wolff, J. Zittartz, Z. Phys. B 41, 43 (1981); W.F. Wolff, P. Hoever, J. Zittartz, Z. Phys. B 42, 259 (1981); P. Hoever, J. Zittartz, Z. Phys. B 44, 129 (1981).
25. P. Hoever, W.F. Wolff, J. Zittartz, Z. Phys. B 41, 43 (1981); W.F. Wolff, P. Hoever, J. Zittartz, Z. Phys. B 42, 259 (1981); P. Hoever, J. Zittartz, Z. Phys. B 44, 129 (1981).
26. R. Shankar, G. Murthy, Phys. Rev. B 36, 536 (1987).
27. T.M. Nieuwenhuizen, H. Orland, Phys. Rev. B 40, 5094 (1989).
28. A.B. Harris, J. Phys. C 7, 1671 (1974).
29. J.M. Luck, J. Stat. Phys. 72, 417 (1993).
30. F. Iglói, J. Phys. A 26, L703 (1993).
31. M. Dekking, M. Mendés-France, A. van der Poorten, Math. Intellig. 4, 130 (1983)
32. B. Berche et al., J. Phys. A 28, L165 (1995).
33. F. Iglói, L. Turban, Phys. Rev. Lett. 77, 1206 (1996).
34. F. Iglói, L. Turban, D. Karevski, F. Szalma, Phys. Rev. B 56, 11031 (1997)
35. J. Hermisson, U. Grimm, M. Baake, J. Phys. A 30, 7315 (1997).
36. F. Iglói, L. Turban, Europhys. Lett. 27, 91 (1994).
37. P.-E. Berche, C. Chatelain, B. Berche, Phys. Rev. Lett. 80, 297 (1998)
38. E. Lieb, T. Schultz, D. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961); P. Pfeuty, Ann. Phys. 57, 79 (1970).
39. E. Lieb, T. Schultz, D. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961); P. Pfeuty, Ann. Phys. 57, 79 (1970).
40. R. Bulirsch, J. Stoer, Num. Math. 6, 413 (1964)
41. M.E. Fisher, P.-G. de Gennes, C. R. Acad. Sci. Paris B 287, 207 (1978).
42. T.W. Burkhardt, T. Xue, Phys. Rev. Lett. 66, 895 (1991); Nucl. Phys. B 354, 653 (1991)
43. T.W. Burkhardt, T. Xue, Phys. Rev. Lett. 66, 895 (1991); Nucl. Phys. B 354, 653 (1991)
44. L. Turban, F. Iglói, J. Phys. A 30, L105 (1997).
45. B. Derrida, A.J. Bray, C. Godrèche, J. Phys. A 27, L357 (1994); B. Derrida, V. Hakim, V. Pasquier, Phys. Rev. Lett. 75, 751 (1995).
46. B. Derrida, A.J. Bray, C. Godrèche, J. Phys. A 27, L357 (1994); B. Derrida, V. Hakim, V. Pasquier, Phys. Rev. Lett. 75, 751 (1995).
47. S.N. Majumdar, C. Sire, Phys. Rev. Lett. 77, 1420 (1996); S.N. Majumdar, C. Sire, A.J. Bray, S.J. Cornell, Phys. Rev Lett. 77, 2867 (1996); S.N. Majumdar, A.J. Bray, S.J. Cornell, C. Sire, Phys. Rev. Lett. 77, 3704 (1996); K. Oerding, S.J. Cornell, A. Bray, Phys. Rev. E 56, R25 (1997); J. Krug, H. Kallabis, S.N. Majumdar, S.J. Cornell, A.J. Bray, C. Sire, Phys. Rev. E 56, 2702 (1997).
48. S.N. Majumdar, C. Sire, Phys. Rev. Lett. 77, 1420 (1996); S.N. Majumdar, C. Sire, A.J. Bray, S.J. Cornell, Phys. Rev Lett. 77, 2867 (1996); S.N. Majumdar, A.J. Bray, S.J. Cornell, C. Sire, Phys. Rev. Lett. 77, 3704 (1996); K. Oerding, S.J. Cornell, A. Bray, Phys. Rev. E 56, R25 (1997); J. Krug, H. Kallabis, S.N. Majumdar, S.J. Cornell, A.J. Bray, C. Sire, Phys. Rev. E 56, 2702 (1997).
49. S.N. Majumdar, C. Sire, Phys. Rev. Lett. 77, 1420 (1996); S.N. Majumdar, C. Sire, A.J. Bray, S.J. Cornell, Phys. Rev Lett. 77, 2867 (1996); S.N. Majumdar, A.J. Bray, S.J. Cornell, C. Sire, Phys. Rev. Lett. 77, 3704 (1996); K. Oerding, S.J. Cornell, A. Bray, Phys. Rev. E 56, R25 (1997); J. Krug, H. Kallabis, S.N. Majumdar, S.J. Cornell, A.J. Bray, C. Sire, Phys. Rev. E 56, 2702 (1997).
50. S.N. Majumdar, C. Sire, Phys. Rev. Lett. 77, 1420 (1996); S.N. Majumdar, C. Sire, A.J. Bray, S.J. Cornell, Phys. Rev Lett. 77, 2867 (1996); S.N. Majumdar, A.J. Bray, S.J. Cornell, C. Sire, Phys. Rev. Lett. 77, 3704 (1996); K. Oerding, S.J. Cornell, A. Bray, Phys. Rev. E 56, R25 (1997); J. Krug, H. Kallabis, S.N. Majumdar, S.J. Cornell, A.J. Bray, C. Sire, Phys. Rev. E 56, 2702 (1997).
51. S.N. Majumdar, C. Sire, Phys. Rev. Lett. 77, 1420 (1996); S.N. Majumdar, C. Sire, A.J. Bray, S.J. Cornell, Phys. Rev Lett. 77, 2867 (1996); S.N. Majumdar, A.J. Bray, S.J. Cornell, C. Sire, Phys. Rev. Lett. 77, 3704 (1996); K. Oerding, S.J. Cornell, A. Bray, Phys. Rev. E 56, R25 (1997); J. Krug, H. Kallabis, S.N. Majumdar, S.J. Cornell, A.J. Bray, C. Sire, Phys. Rev. E 56, 2702 (1997).
52. F. Iglói, H. Rieger, cond-mat/9804316 and cond-mat/9805170, Phys. Rev. E 58 (1998), in press.