Abstract
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, ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$, is coupled linearly to a nonconserved one, ${\mathrm{\ensuremath{\varphi}}}_{\mathit{n}}$, generic power-law decays are induced in the correlations of ${\mathrm{\ensuremath{\varphi}}}_{\mathit{n}}$. When symmetry prevents linear coupling, correlations of the ${\mathrm{\ensuremath{\varphi}}}_{\mathit{n}}$ field decay exponentially under generic conditions, unless ${\mathrm{\ensuremath{\varphi}}}_{\mathit{n}}$ 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.
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