Temporally disordered Ising models

Europhysics Letters

Volumn 56, Issue 4, 2001, Pages 485-491

  Alonso, J J ^a   Munoz M A ^b  

^a UNIVERSITY OF MÁLAGA   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035798514     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2001-00545-8     Document Type: Article

References (43)

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4. STINCHOOMBE R. B., Dilute Magnetism, in Phase Transitions and Critical Phenomena, Vol. 7, edited by DOMB C. and LEBOWITZ J. L. (Academic Press, London) 1983; CARDY J. L., Scaling and Renormalization in Statistical Physics (Cambridge University Press) 1997.
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6. See GRINSTEIN G., Fundamental Problems in Statistical Mechanics VI, edited by COHEN E. G. D. (Elsevier Science) 1985 and references therein. GRINSTEIN G. and LUTHER A., Phys. Rev. B, 13 (1976) 1329; GRINSTEIN G. et al., Phys. Rev. B, 15 (1977) 258.
7. See GRINSTEIN G., Fundamental Problems in Statistical Mechanics VI, edited by COHEN E. G. D. (Elsevier Science) 1985 and references therein. GRINSTEIN G. and LUTHER A., Phys. Rev. B, 13 (1976) 1329; GRINSTEIN G. et al., Phys. Rev. B, 15 (1977) 258.
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11. FUJISAKA H., TUTU H. and RIKVOLD P. A., Phys. Rev. E, 63 (2001) 036109. See also the work by ACHARYYA M., Phys. Rev. E, 59 (1999) 218; 58 (1998) 179.
12. FUJISAKA H., TUTU H. and RIKVOLD P. A., Phys. Rev. E, 63 (2001) 036109. See also the work by ACHARYYA M., Phys. Rev. E, 59 (1999) 218; 58 (1998) 179.
13. FUJISAKA H., TUTU H. and RIKVOLD P. A., Phys. Rev. E, 63 (2001) 036109. See also the work by ACHARYYA M., Phys. Rev. E, 59 (1999) 218; 58 (1998) 179.
14. HARRIS A. B., J. Phys. C, 7 (1974) 1671. The criterion is supported by several RG analysis [4], and has been extended to strong-disorder cases by CHAYES J. T. et al., Phys. Rev. Lett., 57 (1986) 2999.
15. HARRIS A. B., J. Phys. C, 7 (1974) 1671. The criterion is supported by several RG analysis [4], and has been extended to strong-disorder cases by CHAYES J. T. et al., Phys. Rev. Lett., 57 (1986) 2999.
16. As long as the disorder at different sites is uncorrelated, details of the one-site distribution are irrelevant.
17. Using the scaling law vd = 2 - α [12] the relevance criterion can be written in its more familiar form, α > 0.
18. BAUSCH R. et al., Z. Phys. B, 24 (1976) 113.
19. AMIT D., Field Theory, the Renormalization Group and Critical Phenomena (World Scientific) 1984; PARISI G., Statistical Field Theory (Addison Wesley) 1988; ZINN-JUSTIN J., Quantum Field Theory and Critical Phenomena (Oxford Science) 1989.
20. AMIT D., Field Theory, the Renormalization Group and Critical Phenomena (World Scientific) 1984; PARISI G., Statistical Field Theory (Addison Wesley) 1988; ZINN-JUSTIN J., Quantum Field Theory and Critical Phenomena (Oxford Science) 1989.
21. AMIT D., Field Theory, the Renormalization Group and Critical Phenomena (World Scientific) 1984; PARISI G., Statistical Field Theory (Addison Wesley) 1988; ZINN-JUSTIN J., Quantum Field Theory and Critical Phenomena (Oxford Science) 1989.
22. DE DOMINICIS C., Phys. Rev. B, 18 (1978) 4913.
23. Recent results concerning the 2D QRT model can be found in QUEIROZ S. L. A., Comp. Phys. Commun., 121-122 (1999) 210 and references therein . See also BALLESTEROS H. et al., J. Phys. A, 30 (1997) 8379; FRONTERA C. and VIVES E., Phys. Rev. E, 59 (1999) 1295.
24. Recent results concerning the 2D QRT model can be found in QUEIROZ S. L. A., Comp. Phys. Commun., 121-122 (1999) 210 and references therein . See also BALLESTEROS H. et al., J. Phys. A, 30 (1997) 8379; FRONTERA C. and VIVES E., Phys. Rev. E, 59 (1999) 1295.
25. Recent results concerning the 2D QRT model can be found in QUEIROZ S. L. A., Comp. Phys. Commun., 121-122 (1999) 210 and references therein . See also BALLESTEROS H. et al., J. Phys. A, 30 (1997) 8379; FRONTERA C. and VIVES E., Phys. Rev. E, 59 (1999) 1295.
26. Whether QRF in d = 3 defines a unique universality class or there are disorder-distribution dependent RG fixed points is a presently debated issue; although the chances are that there is not a unique RG fixed point. See SOURLAS N., Comp. Phys. Commun., 121-122 (1999) 183; BALLESTEROS H. G. et al., Phys. Rev. B, 58 (1998) 2740; DUXBURY P. M. and MEINKE J. H., cond-mat/0012042. In the infinite-range random field model the exponents depend on the curvature of the disorder distribution, see AHARONY A., Phys. Rev. B, 18 (1978) 3318.
27. Whether QRF in d = 3 defines a unique universality class or there are disorder-distribution dependent RG fixed points is a presently debated issue; although the chances are that there is not a unique RG fixed point. See SOURLAS N., Comp. Phys. Commun., 121-122 (1999) 183; BALLESTEROS H. G. et al., Phys. Rev. B, 58 (1998) 2740; DUXBURY P. M. and MEINKE J. H., cond-mat/0012042. In the infinite-range random field model the exponents depend on the curvature of the disorder distribution, see AHARONY A., Phys. Rev. B, 18 (1978) 3318.
28. Whether QRF in d = 3 defines a unique universality class or there are disorder-distribution dependent RG fixed points is a presently debated issue; although the chances are that there is not a unique RG fixed point. See SOURLAS N., Comp. Phys. Commun., 121-122 (1999) 183; BALLESTEROS H. G. et al., Phys. Rev. B, 58 (1998) 2740; DUXBURY P. M. and MEINKE J. H., cond-mat/0012042. In the infinite-range random field model the exponents depend on the curvature of the disorder distribution, see AHARONY A., Phys. Rev. B, 18 (1978) 3318.
29. Whether QRF in d = 3 defines a unique universality class or there are disorder-distribution dependent RG fixed points is a presently debated issue; although the chances are that there is not a unique RG fixed point. See SOURLAS N., Comp. Phys. Commun., 121-122 (1999) 183; BALLESTEROS H. G. et al., Phys. Rev. B, 58 (1998) 2740; DUXBURY P. M. and MEINKE J. H., cond-mat/0012042. In the infinite-range random field model the exponents depend on the curvature of the disorder distribution, see AHARONY A., Phys. Rev. B, 18 (1978) 3318.
30. This dimensional reduction (PARISI G. and SOURLAS N., Phys. Rev. Lett., 43 (1979) 744) is at odds with the Imry-Ma prediction [17], and it is only recently that this puzzle has been elucidated, see BREZIN E. and DE DOMINICIS C., Europhys. Lett., 44 (1998) 13, and the way in which the perturbative calculation has to be modified put forward; BREZIN E. and DE DOMINICIS C., Europhys. Lett., 44 (1998) 13. See also DOTSENKO V. S., Cond-mat/9809097.
31. This dimensional reduction (PARISI G. and SOURLAS N., Phys. Rev. Lett., 43 (1979) 744) is at odds with the Imry-Ma prediction [17], and it is only recently that this puzzle has been elucidated, see BREZIN E. and DE DOMINICIS C., Europhys. Lett., 44 (1998) 13, and the way in which the perturbative calculation has to be modified put forward; BREZIN E. and DE DOMINICIS C., Europhys. Lett., 44 (1998) 13. See also DOTSENKO V. S., Cond-mat/9809097.
32. This dimensional reduction (PARISI G. and SOURLAS N., Phys. Rev. Lett., 43 (1979) 744) is at odds with the Imry-Ma prediction [17], and it is only recently that this puzzle has been elucidated, see BREZIN E. and DE DOMINICIS C., Europhys. Lett., 44 (1998) 13, and the way in which the perturbative calculation has to be modified put forward; BREZIN E. and DE DOMINICIS C., Europhys. Lett., 44 (1998) 13. See also DOTSENKO V. S., Cond-mat/9809097.
33. This dimensional reduction (PARISI G. and SOURLAS N., Phys. Rev. Lett., 43 (1979) 744) is at odds with the Imry-Ma prediction [17], and it is only recently that this puzzle has been elucidated, see BREZIN E. and DE DOMINICIS C., Europhys. Lett., 44 (1998) 13, and the way in which the perturbative calculation has to be modified put forward; BREZIN E. and DE DOMINICIS C., Europhys. Lett., 44 (1998) 13. See also DOTSENKO V. S., Cond-mat/9809097.
34. IMRY Y. and MA S.-K., Phys. Rev. Lett., 35 (1975) 1399.
35. A similar renormalization attempt for disordered systems in the directed percolation class can be found in JANSSEN H. K., Phys. Rev. E, 55 (1997) 6253.
36. CARDY J. and TAEUBER U., Phys. Rev. Lett., 77 (1996) 4870.
37. ALONSO J. J. and MUÑOZ M. A., Preprint (2000).
38. MARRO J. et al., Phys. Rev. E, 50 (1994) 3237.
39. The existence of continuously changing exponents in: 1) systems in the directed percolation class with this type of disorder (proved numerically and using series expansions in JENSEN I., Phys. Rev. Lett., 77 (1996) 4988); and 2) a one-dimensional model with the same type of disorder [6], supports our belief.
40. ALONSO J. J., LÓPEZ A. I. and MARRO J., Phys. Rev. E, 52 (1995) 6006.
41. A similar situation was studied in [6]: the disorder distribution was bimodal there, and this made the transition be a first-order one.
42. ELMERS H. J., Int. J. Mod. Phys. B, 9 (1995) 3115; SUEN J. S. and ERSKINE J. L., Phys. Rev. Lett., 78 (1997) 3567.
43. ELMERS H. J., Int. J. Mod. Phys. B, 9 (1995) 3115; SUEN J. S. and ERSKINE J. L., Phys. Rev. Lett., 78 (1997) 3567.