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){~}t1/2 for n{≥}3 and L(t){~}t1/4 for n=2. The autocorrelation function A(t) is found to decay with time as A(t){~}t^-(1-λ)/2 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(-at1/2). 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.