DYNAMICAL RELAXATION AND UNIVERSAL SHORT-TIME BEHAVIOR OF FINITE SYSTEMS

A system belonging to the dynamic universality class of model A is considered in a block (V=L(d)) geometry with periodic boundary conditions. The relaxation of the order parameter m(t) from an initial value m(i) is investigated at the bulk critical temperature. We demonstrate that a proper scaling description of the problem involves two characteristic times, t(L) approximately L(z) and t(i) approximately [m(i)]-z/xi, where z is the familiar dynamic bulk exponent, while x(i) is an independent new bulk exponent discovered recently. Previous analyses of the problem either were restricted to t much greater than t(i), or tacitly used the incorrect assumption that x(i) = beta/nu. Thus the short-time regime t much less than t(i) with universal dependence on m(i) was missed. As a concrete example we study the exact solution in the large-n limit.