Analysis of the interface in a nonequilibrium two-temperature Ising model

Physical Review B - Condensed Matter and Materials Physics

Volumn 70, Issue 24, 2004, Pages 1-10

  Hurtado, P I ^a,b   Garrido, P L ^b   Marro, J ^b  

^a Boston University   (United States)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPUTER SIMULATION; KINETICS; MONTE CARLO METHOD; PREDICTION; SURFACE PROPERTY; TEMPERATURE; THEORY;

EID: 14944363550     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.70.245409     Document Type: Article

References (39)

1. D. Jasnow, Rep. Prog. Phys. 47, 1059 (1984).
2. P.G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).
3. D.E. Sullivan and M.M. Telo da Gama, Fluid Interfacial Phenomena, edited by C.A. Croxton, ed. (Wiley, New York, 1986).
4. A.J. Bray, Adv. Phys. 43, 357 (1994).
5. A.-L. Barabási and H.E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).
6. A. Pimpinelli and J. Villain, Physics of Crystal Growth (Cambridge University Press, Cambridge, 1999).
7. D. Bonn and D. Ross, Rep. Prog. Phys. 64, 1085 (2001).
8. A. Hernández-Machado, H. Guo, J.L. Mozos, and D. Jasnow, Phys. Rev. A 39, 4783 (1989).
9. B. Derrida, J.L. Lebowitz, E.R. Speer, and H. Spohn, Phys. Rev. Lett. 67, 165 (1991).
10. J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).
11. P.I. Hurtado, Ph.D. thesis, Universidad de Granada, Granada, Spain, cond-mat/0302349.
12. P.I. Hurtado, J. Marro, and P.L. Garrido (unpublished).
13. P.I. Hurtado, J. Marro, and P.L. Garrido, Phys. Rev. E 70, 021101 (2004).
14. M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986).
15. J.E. Avron, H. van Beijeren, L.S. Schulman, and R.K.P. Zia, J. Phys. A 15, L81 (1982).
16. W.K. Burton, N. Cabrera, and F.C. Frank, Proc. R. Soc. London, Ser. A 243, 299 (1951).
17. S. Miracle-Sole and J. Ruiz, in Micro, Meso and Macroscopic Approaches in Physics, edited by A. Verbeure (Plenum, New York, 1993).
18. P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000).
19. R.A. Blythe and M.R. Evans, Phys. Rev. Lett. 89, 080601 (2002).
20. H.N.V. Temperley, Proc. Cambridge Philos. Soc. 48, 683 (1952).
21. The frozen spins at the top and bottom rows are not taken into account when defining these classes. Since those spins do not change with time, they are considered to be outside the system, just inducing appropriate boundaries conditions. Notice, on the other hand, that an external magnetic field breaks the up-down symmetry, and ten different spin classes then emerge.
22. -Γ] only.
23. η(T,p) as a function of X(T,p), and a trascendental equation for X(T,p) ensues which cannot be solved analytically. The higher order approximation that we present here provides an explicit expression.
24. E. Müller-Hartmann and J. Zittartz, Z. Phys. B 27, 261 (1977).
25. C. van den Broeck, J.M.R. Parrondo, and R. Toral, Phys. Rev. Lett. 73, 3395 (1994); Phys. Rev. E 55, 4084 (1997); J.J. Torres, P.L. Garrido, and J. Marro, Phys. Rev. B 58, 11 488 (1998); W. Genovese, M.A. Muñoz, and P.L. Garrido, Phys. Rev. E 58, 6828 (1998); S. Mangioni, R. Deza, R. Toral, and H. Wio, ibid. 61, 223 (2000); M. Ibañes, J. Garcia-Ojalvo, R. Toral, and J.M. Sancho, Phys. Rev. Lett. 87, 020601 (2001).
26. C. van den Broeck, J.M.R. Parrondo, and R. Toral, Phys. Rev. Lett. 73, 3395 (1994); Phys. Rev. E 55, 4084 (1997); J.J. Torres, P.L. Garrido, and J. Marro, Phys. Rev. B 58, 11 488 (1998); W. Genovese, M.A. Muñoz, and P.L. Garrido, Phys. Rev. E 58, 6828 (1998); S. Mangioni, R. Deza, R. Toral, and H. Wio, ibid. 61, 223 (2000); M. Ibañes, J. Garcia-Ojalvo, R. Toral, and J.M. Sancho, Phys. Rev. Lett. 87, 020601 (2001).
27. C. van den Broeck, J.M.R. Parrondo, and R. Toral, Phys. Rev. Lett. 73, 3395 (1994); Phys. Rev. E 55, 4084 (1997); J.J. Torres, P.L. Garrido, and J. Marro, Phys. Rev. B 58, 11 488 (1998); W. Genovese, M.A. Muñoz, and P.L. Garrido, Phys. Rev. E 58, 6828 (1998); S. Mangioni, R. Deza, R. Toral, and H. Wio, ibid. 61, 223 (2000); M. Ibañes, J. Garcia-Ojalvo, R. Toral, and J.M. Sancho, Phys. Rev. Lett. 87, 020601 (2001).
28. C. van den Broeck, J.M.R. Parrondo, and R. Toral, Phys. Rev. Lett. 73, 3395 (1994); Phys. Rev. E 55, 4084 (1997); J.J. Torres, P.L. Garrido, and J. Marro, Phys. Rev. B 58, 11 488 (1998); W. Genovese, M.A. Muñoz, and P.L. Garrido, Phys. Rev. E 58, 6828 (1998); S. Mangioni, R. Deza, R. Toral, and H. Wio, ibid. 61, 223 (2000); M. Ibañes, J. Garcia-Ojalvo, R. Toral, and J.M. Sancho, Phys. Rev. Lett. 87, 020601 (2001).
29. C. van den Broeck, J.M.R. Parrondo, and R. Toral, Phys. Rev. Lett. 73, 3395 (1994); Phys. Rev. E 55, 4084 (1997); J.J. Torres, P.L. Garrido, and J. Marro, Phys. Rev. B 58, 11 488 (1998); W. Genovese, M.A. Muñoz, and P.L. Garrido, Phys. Rev. E 58, 6828 (1998); S. Mangioni, R. Deza, R. Toral, and H. Wio, ibid. 61, 223 (2000); M. Ibañes, J. Garcia-Ojalvo, R. Toral, and J.M. Sancho, Phys. Rev. Lett. 87, 020601 (2001).
30. C. van den Broeck, J.M.R. Parrondo, and R. Toral, Phys. Rev. Lett. 73, 3395 (1994); Phys. Rev. E 55, 4084 (1997); J.J. Torres, P.L. Garrido, and J. Marro, Phys. Rev. B 58, 11 488 (1998); W. Genovese, M.A. Muñoz, and P.L. Garrido, Phys. Rev. E 58, 6828 (1998); S. Mangioni, R. Deza, R. Toral, and H. Wio, ibid. 61, 223 (2000); M. Ibañes, J. Garcia-Ojalvo, R. Toral, and J.M. Sancho, Phys. Rev. Lett. 87, 020601 (2001).
31. C. Rottman and M. Wortis, Phys. Rev. B 24, 6274 (1981).
32. G. Wulff, Z. Kristallogr. Mineral. 34, 448 (1901); C. Herring, Phys. Rev. 82, 87 (1951); in Structure and Properties of Solid Surfaces, edited by R. Gomer and C.S. Smith (University of Chicago Press, Chicago, 1953), pp. 5-72.
33. G. Wulff, Z. Kristallogr. Mineral. 34, 448 (1901); C. Herring, Phys. Rev. 82, 87 (1951); in Structure and Properties of Solid Surfaces, edited by R. Gomer and C.S. Smith (University of Chicago Press, Chicago, 1953), pp. 5-72.
34. G. Wulff, Z. Kristallogr. Mineral. 34, 448 (1901); C. Herring, Phys. Rev. 82, 87 (1951); in Structure and Properties of Solid Surfaces, edited by R. Gomer and C.S. Smith (University of Chicago Press, Chicago, 1953), pp. 5-72.
35. See Appendix D in Ref. 16.
36. S.C. Glotzer, D. Stauffer, and N. Jan, Phys. Rev. Lett. 72, 4109 (1994); S. Toxvaerd, Phys. Rev. E 53, 3710 (1996); A. Szolnoki, ibid. 60, 2425 (1999); F.J. Alexander, C.A. Laberge, J.L. Lebowitz, and R.K.P. Zia, J. Stat. Phys. 82, 1133 (1996).
37. S.C. Glotzer, D. Stauffer, and N. Jan, Phys. Rev. Lett. 72, 4109 (1994); S. Toxvaerd, Phys. Rev. E 53, 3710 (1996); A. Szolnoki, ibid. 60, 2425 (1999); F.J. Alexander, C.A. Laberge, J.L. Lebowitz, and R.K.P. Zia, J. Stat. Phys. 82, 1133 (1996).
38. S.C. Glotzer, D. Stauffer, and N. Jan, Phys. Rev. Lett. 72, 4109 (1994); S. Toxvaerd, Phys. Rev. E 53, 3710 (1996); A. Szolnoki, ibid. 60, 2425 (1999); F.J. Alexander, C.A. Laberge, J.L. Lebowitz, and R.K.P. Zia, J. Stat. Phys. 82, 1133 (1996).
39. S.C. Glotzer, D. Stauffer, and N. Jan, Phys. Rev. Lett. 72, 4109 (1994); S. Toxvaerd, Phys. Rev. E 53, 3710 (1996); A. Szolnoki, ibid. 60, 2425 (1999); F.J. Alexander, C.A. Laberge, J.L. Lebowitz, and R.K.P. Zia, J. Stat. Phys. 82, 1133 (1996).