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Evolutionary Genomics Group Department of Computational Molecular Biology |
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Title: First-order phase transitions in one-dimensional steady states Authors: Peter F Arndt, Thomas Heinzel, Vladimir Rittenberg Abstract: The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godreche, 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. Reference: Journal of Statistical Physics 90 (1998) 783-815 Links: [Journal] [Fulltext (pdf)] |