Exact multilocal renormalization of the effective action: Application to the random sine Gordon model statics and nonequilibrium dynamics

We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal parts yields a closed exact RG equation for the local part, to a given order in the local part. The method is illustrated on the O(N) model by straightforwardly recovering the eta exponent and scaling functions. Then it is applied to study the glass phase of the Cardy-Ostlund, random phase sine Gordon model near the glass transition temperature. The static correlations and equilibrium dynamical exponent z are recovered and several results are obtained, such as the equilibrium two-point scaling functions. The nonequilibrium, finite momentum, two-time t,t(') response and correlations are computed. They are shown to exhibit scaling forms, characterized by exponents lambda(R)not equallambda(C), as well as universal scaling functions that we compute. The fluctuation dissipation ratio is found to be nontrivial and of the form X[q(z)(t-t(')),t/t(')]. Analogies and differences with pure critical models are discussed.