Renormalization group and perfect operators for stochastic differential equations - art. no. 036125

We develop renormalization group (RG) methods for solving partial and stoch astic differential equations on coarse meshes. RG transformations are used to calculate the precise effect of small-scale dynamics on the dynamics at the mesh size. The fixed point of these transformations yields a perfect op erator: an exact representation of physical observables on the mesh scale w ith minimal lattice artifacts. We apply the formalism to simple nonlinear m odels of critical dynamics, and show how the method leads to an improvement in the computational performance of Monte Carlo methods.