Nonequilibrium structure factor for conserved spin dynamics: Abrupt temperature increase

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

Volumn 54, Issue 3, 1996, Pages 2266-2290

  Luscombe, James H ^a   Luban, Marshall ^b  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4243907373     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.54.2266     Document Type: Article

References (68)

1. J. D. Gunton, M. S. Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic, New York, 1983), Vol. 8, pp. 267-466.
2. H. Furukawa, Adv. Phys. 34, 703 (1985), G. F. Mazenko, O. T. Valls, and M. Zannetti, Phys. Rev. B 38, 520 (1988), and references therein: G. F. Mazenko, Phys. Rev. Lett. 63, 1605 (1989).
3. H. Furukawa, Adv. Phys. 34, 703 (1985), G. F. Mazenko, O. T. Valls, and M. Zannetti, Phys. Rev. B 38, 520 (1988), and references therein: G. F. Mazenko, Phys. Rev. Lett. 63, 1605 (1989).
4. H. Furukawa, Adv. Phys. 34, 703 (1985), G. F. Mazenko, O. T. Valls, and M. Zannetti, Phys. Rev. B 38, 520 (1988), and references therein: G. F. Mazenko, Phys. Rev. Lett. 63, 1605 (1989).
5. K. Binder and D. P. Landau, in Advances in Chemical Physics, edited by I. Prigogine and S. A. Rice (Wiley, New York, 1989), Vol. LXXVI, pp. 91-152.
6. M. C. Tringides, in Chemical Physics of Solid Surfaces, edited by D. A. King and D. P. Woodruff (Elsevier, Amsterdam, 1994), Vol. 7, pp. 215-257.
7. M. C. Tringides, P. K. Wu, and M. G. Lagally, Phys. Rev. Lett. 56, 315 (1987).
8. D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Benjamin, Reading, MA, 1975).
9. J. H. Luscombe, Phys. Rev. B 29, 5142 (1984).
10. See, for example, P. S. Sahni, D. J. Srolovitz, G. S. Grest, M. P. Anderson, and S. A. Safran, Phys. Rev. B 28, 2705 (1983); A. Sadiq and K. Binder, J. Stat. Phys. 35, 5807 (1985); D. A. Huse, Phys. Rev. B 34, 7845 (1986); T. M. Rogers, K. Elder and R. C. Desai, ibid. 37, 9638 (1988).
11. See, for example, P. S. Sahni, D. J. Srolovitz, G. S. Grest, M. P. Anderson, and S. A. Safran, Phys. Rev. B 28, 2705 (1983); A. Sadiq and K. Binder, J. Stat. Phys. 35, 5807 (1985); D. A. Huse, Phys. Rev. B 34, 7845 (1986); T. M. Rogers, K. Elder and R. C. Desai, ibid. 37, 9638 (1988).
12. See, for example, P. S. Sahni, D. J. Srolovitz, G. S. Grest, M. P. Anderson, and S. A. Safran, Phys. Rev. B 28, 2705 (1983); A. Sadiq and K. Binder, J. Stat. Phys. 35, 5807 (1985); D. A. Huse, Phys. Rev. B 34, 7845 (1986); T. M. Rogers, K. Elder and R. C. Desai, ibid. 37, 9638 (1988).
13. See, for example, P. S. Sahni, D. J. Srolovitz, G. S. Grest, M. P. Anderson, and S. A. Safran, Phys. Rev. B 28, 2705 (1983); A. Sadiq and K. Binder, J. Stat. Phys. 35, 5807 (1985); D. A. Huse, Phys. Rev. B 34, 7845 (1986); T. M. Rogers, K. Elder and R. C. Desai, ibid. 37, 9638 (1988).
14. See, for example, Z. W. Lai, G. F. Mazenko, and O. T. Valls, Phys. Rev. B 37, 9481 (1988), and references therein; G. F. Mazenko, O. T. Valls, and F. C. Zhang, ibid 32, 5807 (1985); E. T. Gawlinski, M. Grant, J. D. Gunton, and K. Kaski, ibid. 31, 281 (1985).
15. See, for example, Z. W. Lai, G. F. Mazenko, and O. T. Valls, Phys. Rev. B 37, 9481 (1988), and references therein; G. F. Mazenko, O. T. Valls, and F. C. Zhang, ibid 32, 5807 (1985); E. T. Gawlinski, M. Grant, J. D. Gunton, and K. Kaski, ibid. 31, 281 (1985).
16. See, for example, Z. W. Lai, G. F. Mazenko, and O. T. Valls, Phys. Rev. B 37, 9481 (1988), and references therein; G. F. Mazenko, O. T. Valls, and F. C. Zhang, ibid 32, 5807 (1985); E. T. Gawlinski, M. Grant, J. D. Gunton, and K. Kaski, ibid. 31, 281 (1985).
17. See for example, F. de Pasquale, P. Tartaglia, and P. Tombesi, Phys. Rev. A 31, 2447 (1985); K. Kawasaki and T. Nagai, Physica A 121, 175 (1983); T. Ohta, D. Jasnow, and K. Kawasaki, Phys. Rev. Lett. 49, 1223 (1983).
18. See for example, F. de Pasquale, P. Tartaglia, and P. Tombesi, Phys. Rev. A 31, 2447 (1985); K. Kawasaki and T. Nagai, Physica A 121, 175 (1983); T. Ohta, D. Jasnow, and K. Kawasaki, Phys. Rev. Lett. 49, 1223 (1983).
19. See for example, F. de Pasquale, P. Tartaglia, and P. Tombesi, Phys. Rev. A 31, 2447 (1985); K. Kawasaki and T. Nagai, Physica A 121, 175 (1983); T. Ohta, D. Jasnow, and K. Kawasaki, Phys. Rev. Lett. 49, 1223 (1983).
20. G. F. Mazenko and M. Widom, Phys. Rev. B 25, 1860 (1982).
21. R. J. Glauber, J. Math. Phys. 4, 294 (1963).
22. K. Kawasaki, Phys. Rev. 145, 224 (1966).
23. K. Kawasaki, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1972), Vol. 2, pp. 443-501.
24. See, for example, the review of J. W. Haus and K. W. Kehr, Phys. Rep. 150, 263 (1987).
25. J. W. Evans, Rev. Mod. Phys. 65, 1281 (1993); see also J. W. Evans and D. K. Hoffman, Phys. Rev. B 30, 2704 (1984).
26. J. W. Evans, Rev. Mod. Phys. 65, 1281 (1993); see also J. W. Evans and D. K. Hoffman, Phys. Rev. B 30, 2704 (1984).
27. A. Jesina and M. C. Tringides, Phys. Rev. B 48, 2694 (1993).
28. M. C. Tringides, J. H. Luscombe, and M. G. Lagally, Phys. Rev. B 39, 9377 (1989).
29. J. A. Martin, D. E. Savage, W. Moriz, and M. G. Lagally, Phys. Rev. Lett. 56, 1936 (1986).
30. See, for example, H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971), p. 118.
31. In arriving at the right-hand side of (2.8), we have assumed translational symmetry of the lattice.
32. σ is explicitly time independent.
33. σA.
34. See, for example, I. Oppenheim, K. E. Shuler, and G. H. Weiss, Stochastic Processes in Chemical Physics: The Master Equation (MIT Press, Cambridge, MA, 1977).
35. General properties of master equation operators for kinetic Ising models can be found in G. F. Mazenko and O. T. Valls, in Real Space Renormalization, edited by T. W. Burkhardt and J. M. J. van Leeuwen (Springer-Verlag, Berlin 1982), pp. 87-117; see also, G. F. Mazenko, M. J. Nolan, and O. T. Valls, Phys. Rev. B 22, 1263 (1980).
36. General properties of master equation operators for kinetic Ising models can be found in G. F. Mazenko and O. T. Valls, in Real Space Renormalization, edited by T. W. Burkhardt and J. M. J. van Leeuwen (Springer-Verlag, Berlin 1982), pp. 87-117; see also, G. F. Mazenko, M. J. Nolan, and O. T. Valls, Phys. Rev. B 22, 1263 (1980).
37. S. J. Heilig, J. H. Luscombe, G. F. Mazenko, E. Oguz, and O. T. Valls, Phys. Rev. B 25, 7003 (1982).
38. W. Zwerger, Phys. Lett. A 84, 269 (1981).
39. F. Haake and K. Thol, Z. Phys. B 40, 219 (1980); P. O. Weir, J. M. Kosterlitz, and S. H. Adachi, J. Phys. A 19, L757 (1986).
40. F. Haake and K. Thol, Z. Phys. B 40, 219 (1980); P. O. Weir, J. M. Kosterlitz, and S. H. Adachi, J. Phys. A 19, L757 (1986).
41. G. F. Mazenko and E. Oguz, J. Stat. Phys. 28, 497 (1982).
42. n〉.
43. K. E. Shuler, Phys. Fluids 2, 442 (1959).
44. This scenario was explicitly demonstrated for the two-dimensional Glauber kinetic Ising model in Ref. [7], where, using renormalization group methods, it was shown that the strongly nonequilibrium response to a large and sudden change in magnetic field strength goes over to the predictions of linear-response theory in the long-time limit.
45. See, for example, G. F. Mazenko and O. T. Valls, Phys. Rev. B 24, 1419 (1981).
46. We note that for infinite temperature, it is not strictly necessary to find the memory function; one can solve the equation of motion (2.24) directly in this limit to give (2.43).
47. E. W. Montroll, J. Math, and Phys. 25, 37 (1946).
48. The dynamic critical exponent is given by z =5 for a conserved variable in one dimension; see, for example, J. H. Luscombe, Phys. Rev. B 36, 501 (1987).
49. J. S. Langer, M. Bar-on, and H. D. Miller, Phys. Rev. A 11, 1417 (1975).
50. The notion that nonequilibrium probability distribution functions can be treated as if they were the equilibrium distribution function, except characterized by a time-dependent temperature, has been termed "canonical invariance" by H. C. Andersen, I. Oppenheim, K. E. Shuler, and G. H. Weiss, J. Math. Phys. 5, 522 (1964).
51. The quantity W(q,t) may, however, contribute to higher-order sum rules.
52. See, for example, F. G. Tricomi, Integral Equations (Interscience, New York, 1957).
53. tdτP′(t-τ)G(τ), which is fully equivalent to (3.7).
54. See, for example, E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge University Press, Cambridge, 1927), p. 65.
55. K. Binder, Phys. Rev. B 15, 4425 (1977).
56. See, for example, G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985), Sec. 15.12.
57. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965).
58. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965), Chap. 9.
59. See, for example, M. Luban and J. H. Luscombe, Phys. Rev. B 35, 9045 (1987).
60. Such arguments relating the random walk of domain boundaries to one-dimensional dynamic critical exponents were first introduced by R. Cordery, S. Sarker, and J. Tobochnik, Phys. Rev. B 24, 5402 (1981). These arguments have been extended to the critical dynamics of spins on fractal geometries by J. H. Luscombe and R. C. Desai, ibid. 32, 488 (1985); and J. H. Luscombe, J. Phys. A 20, 1299 (1987).
61. Such arguments relating the random walk of domain boundaries to one-dimensional dynamic critical exponents were first introduced by R. Cordery, S. Sarker, and J. Tobochnik, Phys. Rev. B 24, 5402 (1981). These arguments have been extended to the critical dynamics of spins on fractal geometries by J. H. Luscombe and R. C. Desai, ibid. 32, 488 (1985); and J. H. Luscombe, J. Phys. A 20, 1299 (1987).
62. Such arguments relating the random walk of domain boundaries to one-dimensional dynamic critical exponents were first introduced by R. Cordery, S. Sarker, and J. Tobochnik, Phys. Rev. B 24, 5402 (1981). These arguments have been extended to the critical dynamics of spins on fractal geometries by J. H. Luscombe and R. C. Desai, ibid. 32, 488 (1985); and J. H. Luscombe, J. Phys. A 20, 1299 (1987).
63. J. H. Luscombe and M. Luban, Surf. Sci. (to be published).
64. J. H. Luscombe and M. Luban (unpublished).
65. N. B. Ninham, R. Nossal, and R. Zwanzig, J. Chem. Phys. 51, 5028 (1969).
66. 1(z/2)] which follows upon using formulas in Sec. 13.4 of that reference.
67. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge University Press, Cambridge, 1958).
68. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), Sec. 6.4.