Universality in the off-equilibrium critical dynamics of the three-dimensional diluted Ising model

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 5, 1999, Pages 5198-5201

  Parisi, G ^a   Ricci Tersenghi, F ^a   Ruiz Lorenzo, J J ^b  

^a UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

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[No Author keywords available]

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ARTICLE;

EID: 0000454735     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.5198     Document Type: Article

References (23)

1. For what the equilibrium dynamical exponent concerns, a very interesting historical review can be found (especially p. 301 and thereafter) in the paper by H.-O. Heuer, in Annual Review of Computational Physics IV, edited by D. Stauffer (World Scientific, Singapore, 1996), pp. 267–315.
2. H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, J. J. Ruiz-Lorenzo, and G. Parisi, Phys. Rev. B 58, 2740 (1998).
3. A. Aharony, Phys. Rev. B 13, 2092 (1976).
4. D. P. Belanger , J. Phys. (Paris) Colloq. 49, C8-1229 (1988).
5. S.-K. Ma, Modern Theory of Critical Phenomena (W. A. Benjamin, Inc., Reading, MA, 1976).
6. G. Grinstein, S.-K. Ma, and G. F. Mazenko, Phys. Rev. B 15, 258 (1977).
7. V. V. Prudnikov and A. N. Vakilov, Zh. Éksp. Teor. Fiz. 101, 1853 (1992) [Sov. Phys. JETP 74, 990 (1992)].
8. H. K. Janssen, K. Oerding, and E. Sengespeick, J. Phys. A 28, 6073 (1995).
9. H.-O. Heuer, J. Phys. A 26, L341 (1993).
10. The dynamical critical exponent measured out-of-equilibrium and in-equilibrium should be the same. This fact has been shown, using an (Formula presented) expansion, in H. K. Janssen, B. Schaub, and B. Schmittmann, Z. Phys. 73, 539 (1989).
11. H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, J. J. Ruiz-Lorenzo, and G. Parisi, Phys. Lett. B 400, 346 (1997).
12. M. Henkel, S. Andrieu, Ph. Bauer, and M. Piecuch, Phys. Rev. Lett. 80, 4783 (1998).
13. The advantage of the off-equilibrium measurements is that, as long as (Formula presented) [where (Formula presented) is the off-equilibrium correlation length], the system size can be considered infinite for all the practical purposes.
14. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. J. Teller, J. Chem. Phys. 21, 1087 (1953).
15. R. Folk, Yu. Holovatch, and T. Yavors’kii, Zh. Eksp. Teor. Fiz. 69, 698 (1999) [JETP Lett. 69, 747 (1999)].
16. Z. Slanič, D. P. Belanger, and J. A. Fernandez-Baca, Phys. Rev. Lett. 82, 426 (1999).
17. The interested reader can obtain formulas up to five loops in the paper of H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995).
18. J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics Vol. 5 (Cambridge University Press, Cambridge, 1996).
19. See Ref. 18, p. 152. In particular, Cardy shows that to order (Formula presented) the eigenvalue associated with the magnetic field (Formula presented) remains unchanged if dilution is added to the system. Remember that (Formula presented) where d is the dimensionality of the space.
20. CERNLIB. CERN program library (CERN, Geneva, Switzerland, 1996).
21. The summability of the perturbative expansions in diluted system is a complex issue. At least, in zero dimensions it is possible to show that the perturbative series of the free energy lacks Borel summability. See, for example, A. J. Bray, T. McCarthy, M. A. Moore, J. D. Reger, and A. P. Young, Phys. Rev. B 36, 2212 (1987)
22. Phys. Rev. BA. J. McKane, 49, 12 003 (1994).This could explain the bad convergence of the (Formula presented) expansion in diluted systems. See, for (Formula presented) also 15 and 22.
23. Vik. Dotsenko, J. Phys. A 32, 2949 (1999).