Joel L. Lebowitz, Claudia Neuhauser and Krishnamurthi Ravishankar
Dynamics of a Spin-Exchange Model
(61K, TeX)
ABSTRACT. We study a model on the non-negative half line ${\bf Z}_0^+$, $\lbrace
0,1,2,\dots\rbrace $ in which particles created at the origin at rate 1
jump to the right at rate 1. If a particle jumps onto an already occupied
site the two particles annihilate each other. In addition, whenever a
particle jumps its closest neighbor to the right jumps along with it. We
find that the spatial decay rate of the particle density in the stationary
state is of order $1/\sqrt{x}$ at distance $x$ from the origin. This model
provides an approximation to the dynamics of an anchored Toom interface
which can be represented as a spin-exchange model.