Universal Short-Time Behavior in Critical Dynamics near Surfaces

Abstract

We study the time evolution of classical spin systems with purely relaxational dynamics, quenched from T >> T_c to the critical point, in the semi-infinite geometry. Shortly after the quench, like in the bulk, a nonequilibrium regime governed by universal power laws is also found near the surface. We show for `ordinary' and `special' transitions that the corresponding critical exponents differ from their bulk values, but can be expressed via scaling relations in terms of known bulk and surface exponents. To corroborate our scaling analysis, we present perturbative (epsilon-expansion) and Monte Carlo results.