G. Grinstein et al., SCALE-INVARIANCE OF NONCONSERVED QUANTITIES IN DRIVEN SYSTEMS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 48(2), 1993, pp. 180000643-180000646
Noisy nonequilibrium systems involving locally conserved quantities ty
pically exhibit generic scale invariance-infinite correlation lengths
and the associated algebraic decay of correlations without the tuning
of external parameters. It is shown here that if such a conserved fiel
d, phi(c), is coupled linearly to a nonconserved one, phi(n), generic
power-law decays are induced in the correlations of phi(n). When symme
try prevents linear coupling, correlations of the phi(n) field decay e
xponentially under generic conditions, unless phi(n) experiences a bro
ken symmetry, in which case linear coupling and hence algebraic decays
can be generated. Numerical support for these results in simple conse
rving coupled map lattices is presented.