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The Application of the Yang–Lee Theory to Study a Phase Transition in a Non-Equilibrium System

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Abstract

We study a phase transition in a non-equilibrium model first introduced in ref. 5, using the Yang–Lee description of equilibrium phase transitions in terms of both canonical and grand canonical partition function zeros. The model consists of two different classes of particles hopping in opposite directions on a ring. On the complex plane of the diffusion rate we find two regions of analyticity for the canonical partition function of this model which can be identified by two different phases. The exact expressions for both distribution of the canonical partition function zeros and their density are obtained in the thermodynamic limit. The fact that the model undergoes a second-order phase transition at the critical point is confirmed. We have also obtained the grand canonical partition function zeros of our model numerically. The similarities between the phase transition in this model and the Bose–Einstein condensation has also been studied.

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REFERENCES

  1. B. Schmittmann and R. K. P. Zia, in Phase Transitions and Critical Phenomena, Vol. 17, C. Domb and J. Lebowitz, eds. (Academic Press, London, 1995).

    Google Scholar 

  2. G. M. Schütz, Integrable stochastic processes, in Phase Transitions and Critical Phenomena, Vol. 19, C. Domb and J. Lebowitz, eds. (Academic Press, New York, 1999).

    Google Scholar 

  3. C. N. Yang and T. D. Lee, Phys. Rev. 87:404(1952)

    Google Scholar 

  4. C. N. Yang and T. D. LeePhys. Rev. 87:410(1952).

    Google Scholar 

  5. S. Grossmann and W. Rosenhauer, Z. Phys. 218:437(1969)

    Google Scholar 

  6. S. Grossmann and V. Lehmann, Z. Phys. 218:449(1969).

    Google Scholar 

  7. F. H. Jafarpour, J. Phys. A: Math. Gen. 33:8673(2000).

    Google Scholar 

  8. P. F. Arndt, Phys. Rev. Lett. 84:814(2000).

    Google Scholar 

  9. R. A. Blythe and M. R. Evans, Phys. Rev. Lett. 89, 080601(2002).

    Google Scholar 

  10. P. F. Arndt, T. Heinzel, and V. Rittenberg, J. Stat. Phys. 97:1(1999).

    Google Scholar 

  11. M. R. Evans, Europhys. Lett. 36:13(1996).

    Google Scholar 

  12. G. M. Schütz and E. Domany, J. Stat. Phys. 72:277(1993)

    Google Scholar 

  13. B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, J. Phys. A 26:1493(1993).

    Google Scholar 

  14. B. Derrida, S. A. Janowsky, J. L. Lebowitz, and E. R. Speer, J. Stat. Phys. 78:813(1993).

    Google Scholar 

  15. R. K. Pathria, Statistical Physics (Oxford, Pergamon, 1972).

    Google Scholar 

  16. K. Mallick, J. Phys. A: Math. Gen. 29:5375(1996)

    Google Scholar 

  17. H.-W. Lee, V. Popkov, and D. Kim, J. Phys. A: Math. Gen. 30:8497(1997)

    Google Scholar 

  18. G. M. Schütz, J. Stat. Phys. 71:471(1993).

    Google Scholar 

  19. F. H. Jafarpour, Cond-mat/0301407 (to appear in J. Phys. A: Math. Gen.).

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Authors and Affiliations

  1. Physics Department, Bu-Ali Sina University, Hamadan, Iran

    Farhad H. Jafarpour

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  1. Farhad H. Jafarpour
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Jafarpour, F.H. The Application of the Yang–Lee Theory to Study a Phase Transition in a Non-Equilibrium System. Journal of Statistical Physics 113, 269–281 (2003). https://doi.org/10.1023/A:1025731006690

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