Growth of order in vector spin systems; scaling and universality

Publisher Website
Google Scholar
Abstract
The growth of order in vector spin systems with nonconserved 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 2n5 are presented. For n4, a scaling regime (where a characteristic length scale L(t) emerges) is entered for sufficiently long times, with L(t)t12/. The autocorrelation function. A(t) decays with time as A(t)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). For n4, universal amplitudes and scaling functions characterizing the energy relaxation and the equal-time correlation function are identified. It is argued that for d3, where an ordered phase exists at low temperature, such universal quantities characterize the entire ordered phase.