Scaling properties in off-equilibrium dynamical processes

In this paper, we analyze the consequences of scaling hypotheses on dynamic functions, such as two-time correlations C(t,t'). We show, under general conditions, that C(t,t') must obey the scaling behavior C(t,t') = phi(1)(t)(f(beta))S(beta), where the scaling variable is beta=beta(phi(1)(t')/phi(1)(t)) and phi(1)(t'),phi(1)(t) are two undetermined functions. The presence of a nonconstant exponent f(beta) signals the appearance of multiscaling properties in the dynamics. [S1063-651X(99)15003-7].