Growth of order in vector spin systems and self-organized criticality

We consider the process of zero-temperature ordering in a vector-spin system, with nonconserved order parameter (model A), following an instantaneous quench from infinite temperature. We present the results of numerical simulations in one spatial dimension for spin dimension n in the range 2≤n≤5. We find that a scaling regime [where a characteristic-length scale L(t) emerges] is entered in all cases for sufficiently long times with L(t)∼${\mathit{t}}^{1/2}$ for n≥3 and L(t)∼${\mathit{t}}^{1/4}$ for n=2. The autocorrelation function A(t) is found to decay with time as A(t)∼${\mathit{t}}^{\mathrm{-}(1\mathrm{}\mathrm{-}\lambda )/2\mathrm{}}$ for n≥3, where λ is a new n-dependent exponent at the T=0 fixed point (as predicted in a recent 1/n expansion). For n=2, A(t)∼exp(-${\mathit{at}}^{1/2}$). We give simple analytical arguments explaining the anomalous behavior found for n=2. We also discuss the new exponents at the T=0 fixed point in the wider context of self-organizing systems.