 
Summary: Journal of Statistical Physics, Vol. 97, Nos. 1Â2, 1999
Spontaneous Breaking of Translational Invariance and
Spatial Condensation in Stationary States on a Ring.
I. The Neutral System
Peter F. Arndt,1, 3
Thomas Heinzel,1
and Vladimir Rittenberg1, 2
Received September 15, 1998; final May 18, 1999
We consider a model in which positive and negative particles with equal den
sities diffuse in an asymmetric, CPinvariant way on a ring. The positive par
ticles hop clockwise, the negative counterclockwise, and oppositely charged
adjacent particles may swap positions. The model depends on two parameters.
Analytic calculations using quadratic algebras, inhomogeneous solutions of the
meanfield equations, and Monte Carlo simulations suggest that the model has
three phases: (1) a pure phase in which one has three pinned blocks of only
positive or negative particles and vacancies and in which translational
invariance is broken; (2) a mixed phase in which the current has a linear
dependence on one parameter, but is independent of the other one and of the
density of the charged particles; in this phase one has a bump and a fluid, the
bump (condensate) containing positive and negative particles only, the fluid
