Scale invariance of nonconserved quantities in driven systems

Noisy nonequilibrium systems involving locally conserved quantities typically 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 field, ${\mathrm{\phi }}_{\mathit{c}}$, is coupled linearly to a nonconserved one, ${\mathrm{\phi }}_{\mathit{n}}$, generic power-law decays are induced in the correlations of ${\mathrm{\phi }}_{\mathit{n}}$. When symmetry prevents linear coupling, correlations of the ${\mathrm{\phi }}_{\mathit{n}}$ field decay exponentially under generic conditions, unless ${\mathrm{\phi }}_{\mathit{n}}$ experiences a broken symmetry, in which case linear coupling and hence algebraic decays can be generated. Numerical support for these results in simple conserving coupled map lattices is presented.