Abstract
The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godrèche, and Mukamel are studied using Monte Carlo simulations. We show that mean-field theory does not give the correct phase diagram. On the first-order phase transition line which separates the CP-symmetric phase from the broken phase, the density profiles can be understood through an unexpected pattern of shocks. In the broken phase the free energy functional is not a convex function, but looks like a standard Ginzburg–Landau picture. If a symmetry-breaking term is introduced in the boundaries, the Ginzburg–Landau picture remains and one obtains spinodal points. The spectrum of the Hamiltonian associated with the master equation was studied using numerical diagonalization. There are massless excitations on the first-order phase transition fine with a dynamical critical exponent z = 2, as expected from the existence of shocks, and at the spinodal points, where we find z = 1. It is the first time that this value, which characterizes conformal invariant equilibrium problems, appears in stochastic processes.
Similar content being viewed by others
REFERENCES
J. Krug, Phys. Rev. Lett. 67:1882 (1991).
B. Derrida, E. Domany, and D. Mukamel, J. Stat. Phys. 69:667 (1992).
B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, J. Phys. A: Math. Gen. 26:1493 (1993).
G. Schutz and E. Domany, J. Stat. Phys. 72:277 (1993).
P. P. Martin, Potts models and related problems in statistical mechanics (World Scientific, Singapore).
M. R. Evans, D. P. Foster, C. Godrèche, and D. Mukamel, Phys. Rev. Lett. 74:208 (1995).
M. R. Evans, D. P. Foster, C. Godrèche, and D. Mukamel, J. Stat. Phys. 80:69 (1995).
F. H. L. Eßler, and V. Rittenberg, J. Phys. A: Math. Gen. 29:3375 (1996).
S. Sandow, Phys. Rev. E50:2660 (1994).
R. B. Griffiths, C.-Y. Weng, and J. S. Langer, Phys. Rev. 149:301; J. D. Gunton, M. San Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic Press), Vol. 8, p. 267, 1989.
M. den Nijs, in Proceedings of the 4th workshop on Statistical Physics, Seoul, January 27–31 (1997).
J. L. Lebowitz, E. Presusti, and H. Spohn, J. Stat. Phys. 51:841 (1988).
K. Mallick, Ph.D. thesis, Saclay (1996).
C. H. Bennett and G. Grinstein, Phys. Rev. Lett. 55:657 (1985).
V. Privman and L. S. Schulman, J. Phys. A: Math. Gen. 15:L238 (1982), and J. Stat. Phys. 29:205.
U. Bilstein, diploma thesis, BONN-IB-96-33 (1996).
R. Bulirsch and J. Stoer, Numer. Math. 6:413 (1964), M. Henkel and G. Schütz, J. Phys. A: Math. Gen. 21:2617 (1988).
M. Le Bellac, Quantum and statistical field theory (Oxford University Press, Oxford, 1991).
P. F. Arndt and T. Heinzel, cond-mat 9710287 (1997).
C. Godrèche, J. M. Luck, M. R. Evans, D. Mukamel, S. Sandow, and S. R. Speer, J. Phys. A: Math. Gen. 28:6039 (1995).
U. Bilstein and B. Wehefritz, J. Phys. A: Math. Gen. 30:4925 (1997).
F. C. Alcaraz, S. Dasmahapatra, and V. Rittenberg, cond-mat 9705172 (1997).
G. Schütz, Phys. Rev. E47:4265 (1993).
S. A. Janowsky and J. L. Lebowitz, Phys. Rev. A45:618 (1992).
G. Schütz, J. Stat. Phys. 71:471 (1993).
K. Mallick, J. Phys. A: Math. Gen. 29:5375 (1996).
K. Krebs, to be published (1997).
G. von Gehlen and V. Rittenberg, J. Phys. A: Math. Gen. 19:L625 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Arndt, P.F., Heinzel, T. & Rittenberg, V. First-Order Phase Transitions in One-Dimensional Steady States. Journal of Statistical Physics 90, 783–815 (1998). https://doi.org/10.1023/A:1023229004414
Issue Date:
DOI: https://doi.org/10.1023/A:1023229004414