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Domain Number Distribution in the Nonequilibrium Ising Model

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Abstract

We study domain distributions in the one-dimensional Ising model subject to zero-temperature Glauber and Kawasaki dynamics. The survival probability of a domain, S(t)∼t −ψ, and an unreacted domain, Q 1(t)∼t −δ, are characterized by two independent nontrivial exponents. We develop an independent interval approximation that provides close estimates for many characteristics of the domain length and number distributions including the scaling exponents.

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REFERENCES

  1. A. J. Bray, Adv. Phys. 43:357 (1994).

    Google Scholar 

  2. D. S. Fisher and D. A. Huse, Phys. Rev. B 38:373 (1988).

    Google Scholar 

  3. B. Derrida, A. J. Bray, and C. Godrèche, J. Phys. A 27:L357 (1994).

    Google Scholar 

  4. P. L. Krapivsky, E. Ben-Naim, and S. Redner, Phys. Rev. E 50:2474 (1994).

    Google Scholar 

  5. A. J. Bray, B. Derrida, and C. Godrèche, Europhys. Lett. 27:175 (1994).

    Google Scholar 

  6. B. Derrida, V. Hakim, and V. Pasquier, Phys. Rev. Lett. 75:751 (1995); J. Stat. Phys. 85:763 (1996).

    Google Scholar 

  7. E. Ben-Naim, L. Frachebourg, and P. L. Krapivsky, Phys. Rev. E 53:3078 (1996).

    Google Scholar 

  8. S. N. Majumdar and C. Sire, Phys. Rev. Lett. 77:1420 (1996).

    Google Scholar 

  9. S. N. Majumdar, A. J. Bray, C. Cornell, and C. Sire, Phys. Rev. Lett. 77:3704 (1996).

    Google Scholar 

  10. B. Derrida, Phys. Rev. E 55:3705 (1997).

    Google Scholar 

  11. B. P. Lee and A. D. Rutenberg, Phys. Rev. Lett. 79:4842 (1997).

    Google Scholar 

  12. B. Yurke, A. N. Pargellis, S. N. Majumdar, and C. Sire, Phys. Rev. E 56:40 (1997).

    Google Scholar 

  13. J. Cardy, J. Phys. A 28:L19 (1995).

    Google Scholar 

  14. P. L. Krapivsky, S. Redner, and F. Leyvraz, Phys Rev. E 51:3977 (1995).

    Google Scholar 

  15. E. Ben-Naim, Phys. Rev. E 53:1566 (1996); M. Howard, J. Phys. A 29:3437 (1996); C. Monthus, Phys. Rev. E 54:4844 (1996).

    Google Scholar 

  16. S. N. Majumdar and C. Cornell, cond-mat/9707344.

  17. L. Frachebourg, P. L. Krapivsky, and E. Ben-Naim, Phys. Rev. Lett. 77:2125 (1996); Phys. Rev. E 54:6186 (1996).

    Google Scholar 

  18. L. Frachebourg and P. L. Krapivsky, Phys. Rev. E 55:252 (1997).

    Google Scholar 

  19. S. N. Marcos-Martin, D. Beysens, J. P. Bouchaud, C. Godrèche, and I. Yekutieli, Physica A 214:396 (1996).

    Google Scholar 

  20. B. Levitan and E. Domany, Europhys. Lett. 38:485 (1997).

    Google Scholar 

  21. S. N. Majumdar, C. Sire, A. J. Bray, and S. J. Cornell, Phys. Rev. Lett. 77:2867 (1996); B. Derrida, V. Hakim, and R. Zeitak, Phys. Rev. Lett. 77:2871 (1996).

    Google Scholar 

  22. A. Watson, Science 274:919 (1996).

    Google Scholar 

  23. E. Ising, Z. Phys. 31:253 (1925).

    Google Scholar 

  24. R. J. Glauber, J. Math. Phys. 4:294 (1963).

    Google Scholar 

  25. K. Kawasaki, Phys. Rev. 145:224 (1966).

    Google Scholar 

  26. P. L. Krapivsky and E. Ben-Naim, Phys. Rev. E 56:3788 (1997).

    Google Scholar 

  27. F. Y. Wu, Rev. Mod. Phys. 54:235 (1982).

    Google Scholar 

  28. For a review of cellular structures see J. Stavans, Rep. Prog. Phys. 56:733 (1993).

    Google Scholar 

  29. S. K. Kurtz and F. M. A. Carpay, J. Appl. Phys. 51:5725 (1981).

    Google Scholar 

  30. J. A. Glazier, M. P. Anderson, and G. S. Grest, Philos. Mag. B 62:615 (1990); H. Flyvbjerg, Phys. Rev. E 47:4037 (1993).

    Google Scholar 

  31. K. L. Babcock and R. M. Westervelt, Phys. Rev. Lett. 64:2168 (1990).

    Google Scholar 

  32. D. ben-Avraham, M. A. Burscka, and C. R. Doering, J. Stat. Phys. 60:695 (1990).

    Google Scholar 

  33. Z. Racz, Phys. Rev. Lett. 55:1707 (1985).

    Google Scholar 

  34. J. Amar and F. Family, Phys. Rev. A 41:3258 (1990).

    Google Scholar 

  35. P. A. Alemany and D. ben-Avraham, Phys. Lett. A 206:18 (1995).

    Google Scholar 

  36. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill Book Co., Singapore, 1984).

    Google Scholar 

  37. B. Derrida and R. Zeitak, Phys. Rev. E 54:2513 (1996).

    Google Scholar 

  38. E. Ben-Naim and P. L. Krapivsky, Phys. Rev. E 53:291 (1996).

    Google Scholar 

  39. R. Cordery, S. Sarker, and J. Tobochnik, Phys. Rev. B 24:5402 (1981).

    Google Scholar 

  40. S. J. Cornell, K. Kaski, and R. B. Stinchcombe, Phys. Rev. B 44:12263 (1991).

    Google Scholar 

  41. S. N. Majumdar and D. A. Huse, Phys. Rev. E 52:270 (1995).

    Google Scholar 

  42. A. Levy, S. Reich, and P. Meakin, Phys. Lett. A 87:248 (1982); P. Meakin and S. Reich, Phys. Lett. A 92:247 (1982).

    Google Scholar 

  43. Y. Elskens and H. L. Frisch, J. Stat. Phys. 48:1243 (1987); V. Privman, Phys. Rev. Lett. 69:3686 (1993); P. L. Krapivsky, J. Stat. Phys. 74:1211 (1994).

    Google Scholar 

  44. R. G. Palmer and H. L. Frisch, J. Stat. Phys. 38:867 (1985); S. N. Majumdar and C. Sire, Phys. Rev. Lett. 70:4022 (1993).

    Google Scholar 

  45. A. Sadiq and K. Binder, J. Stat. Phys. 35:517 (1984).

    Google Scholar 

  46. W. Feller, An Introduction to Probability Theory, Vol. 1 (Wiley, New York, 1971).

    Google Scholar 

  47. W. Y. Tam, R. Zeitak, K. Y. Szeto, and J. Stavans, Phys. Rev. Lett. 78:1588 (1997).

    Google Scholar 

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Authors and Affiliations

  1. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico

    E. Ben-Naim

  2. Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts, 02215

    P. L. Krapivsky

Authors
  1. E. Ben-Naim
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  2. P. L. Krapivsky
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Ben-Naim, E., Krapivsky, P.L. Domain Number Distribution in the Nonequilibrium Ising Model. Journal of Statistical Physics 93, 583–601 (1998). https://doi.org/10.1023/B:JOSS.0000033243.27556.99

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  • DOI: https://doi.org/10.1023/B:JOSS.0000033243.27556.99

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