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Phase transitions and universality in nonequilibrium steady states of stochastic Ising models

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Abstract

We present results of direct computer simulations and of Monte Carlo renormalization group (MCRG) studies of the nonequilibrium steady states of a spin system with competing dynamics and of the voter model. The MCRG method, previously used only for equilibrium systems, appears to give useful information also for these nonequilibrium systems. The critical exponents are found to be of Ising type for the competing dynamics model at its second-order phase transitions, and of mean-field type for the voter model (consistent with known results for the latter).

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References

  1. G. Vichniac,Physica 10D:117 (1984); G. Vichniac, inDisordered Systems and Biological Organization, B. Bienenstock, F. Fogelman Soulie, and G. Weisbuch, eds. (Springer-Verlag, Berlin, 1986); S. Wolfram,Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).

    Google Scholar 

  2. T. M. Liggett,Interacting Particle Systems (Springer, Berlin, 1985), and references therein.

    Google Scholar 

  3. H. Künsch,Z. Wahrsch. Verw. Gebiete 66:407 (1984).

    Google Scholar 

  4. S. Katz, J. L. Lebowitz, and H. Spohn,Phys. Rev. B 28:1655 (1983);J. Stat. Phys. 34:497 (1984).

    Google Scholar 

  5. H. van Beijeren and L. S. Schulman,Phys. Rev. Lett. 53:806 (1984).

    Google Scholar 

  6. J. Krug, J. L. Lebowitz, H. Spohn, and M. Q. Zhang,J. Stat. Phys. 44:535 (1986).

    Google Scholar 

  7. P. L. Garrido, A. Labarta, and J. Marro,J. Stat. Phys. 49:551 (1987).

    Google Scholar 

  8. J. M. Gonzalez-Miranda, P. L. Garido, J. Marro, and Joel L. Lebowitz,Phys. Rev. Lett. 59:1934 (1987).

    Google Scholar 

  9. A. De Masi, P. A. Ferrari, and J. L. Lebowitz,Phys. Rev. Lett. 55:1947 (1985);J. Stat. Phys. 44:589 (1986).

    Google Scholar 

  10. J. L. Lebowitz,Physica 140A:232 (1986).

    Google Scholar 

  11. M. Q. Zhang, One-dimensional competing dynamics, Preprint (1987).

  12. G. Grinstein, C. Jayaprakash, and Yu He,Phys. Rev. Lett. 55:2527 (1985).

    Google Scholar 

  13. K. Kawasaki, inPhase Transition and Critical Phenomena, Vol. 4, C. Domb and M. S. Green, eds. (Academic Press, London, 1972).

    Google Scholar 

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

    Google Scholar 

  15. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller,J. Chem. Phys. 21:1087 (1953).

    Google Scholar 

  16. R. Dickman,Phys. Lett. A 122:463 (1987).

    Google Scholar 

  17. R. H. Swendsen,Phys. Rev. Lett. 42:859 (1979).

    Google Scholar 

  18. R. H. Swendsen, inPhase Transitions, M. Levy, J.-C. Guilou, and J. Zinn-Justin, eds. (Plenum Press, New York, 1982).

    Google Scholar 

  19. R. H. Swendsen, inReal Space Renormalization, T. W. Burkhardt and J. M. J. van Leeuwen, eds. (Springer, Berlin, 1982).

    Google Scholar 

  20. S.-K. Ma,Modern Theory of Critical Phenomena (Benjamin, Reading, Massachusetts, 1976).

    Google Scholar 

  21. J. L. Lebowitz and H. Saleur,Physica 138A:194 (1986).

    Google Scholar 

  22. E. Presutti and H. Spohn,Ann. Prob. 11:867 (1983).

    Google Scholar 

  23. Th. Niemeijer and J. M. J. Van Leeuwen, inPhase Transitions and Critical Phenomena, Vol. 6, C. Domb and M. S. Green, eds. (Academic, New York, 1976).

    Google Scholar 

  24. C. Maes and R. Schonmann, Private communication.

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Wang, J.S., Lebowitz, J.L. Phase transitions and universality in nonequilibrium steady states of stochastic Ising models. J Stat Phys 51, 893–906 (1988). https://doi.org/10.1007/BF01014891

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