Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark

We derive the necessary conditions for implementing a regulator that depends on both momentum and frequency in the nonperturbative renormalization group flow equations of out-of-equilibrium statistical systems. We consider model A as a benchmark and compute its dynamical critical exponent $z$. This allows us to show that frequency regulators compatible with causality and the fluctuation-dissipation theorem can be devised. We show that when the Principle of Minimal Sensitivity (PMS) is employed to optimize the critical exponents $\eta$, $\nu$ and $z$, the use of frequency regulators becomes necessary to make the PMS a self-consistent criterion.Comment: 11 pages, 6 figure

Quantitative Phase Diagrams of Branching and Annihilating Random Walks

We demonstrate the full power of nonperturbative renormalisation group methods for nonequilibrium situations by calculating the quantitative phase diagrams of simple branching and annihilating random walks and checking these results against careful numerical simulations. Specifically, we show, for the 2A->0, A -> 2A case, that an absorbing phase transition exists in dimensions d=1 to 6, and argue that mean field theory is restored not in d=3, as suggested by previous analyses, but only in the limit d -> $\infty$.Comment: 4 pages, 3 figures, published version (some typos corrected