GROWTH OF ORDER IN VECTOR SPIN SYSTEMS - SCALING AND UNIVERSALITY

The growth of order in vector spin systems with non-conserved order parameter (`model A') is considered following an instantaneous quench from infinite to zero temperature. The results of numerical simulations in spatial dimension d = 2 and spin dimension 2 less-than-or-equal-to n less-than-or-equal-to 5 are presented. For n greater-than-or-equal-to 4, a scaling regime (where a characteristic length scale L(t) emerges) is entered for sufficiently long times, with L(t) approximately t1/2. The autocorrelation function A(t) decays with time as A(t) approximately t-(d-lambda)/2, and the exponent lambda(n) agrees well with the predictions of the 1/n-expansion. The cases n = 2 and 3 are more complicated, due to the non-trivial role played by topological singularities, i.e. vortices (n = 2) and Polyakov solitons (n = 3). Fo r n greater-than-or-equal-to 4, universal amplitudes and scaling functions characterizing the energy relaxation and the equal-time correlation function are identified. It is argued that for d greater-than-or-equal-to 3, where an ordered phase exists at low temperature, such universal quantities characterize the entire ordered phase.