 
Summary: Journal of Statistical Physics, Vol. 90, Nos. 3/4, 1998
FirstOrder Phase Transitions in OneDimensional
Steady States
Peter F. Arndt,1'2 Thomas Heinzel,1 2 and VladimirRittenberg12
Received July 31, 1997:final November 6, 1997
The steady states of the twospecies (positive and negative particles) asymmetric
exclusion model of Evans, Foster, Godreche, and Mukamel are studied using
Monte Carlo simulations. We show that meanfield theory does not give the
correct phase diagram. On the firstorder phase transition line which separates
the CPsymmetric 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
GinzburgLandau picture. If a symmetrybreaking term is introduced in the
boundaries, the GinzburgLandau 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 firstorder 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
: = 1. It is the first time that this value, which characterizes conformalinvariant
equilibrium problems, appears in stochastic processes.
