Numerical coarse-graining of fluid field theories

We present a formalism for the systematic numerical coarse-graining of field-theoretic models of fluids that draws upon techniques from both the Monte Carlo renormalization group and particle-based coarse-graining literature. A force-matching technique initially developed for coarse-graining particle-based interaction potentials is adapted to calculate renormalized field-theoretic coupling coefficients in a complex-valued field theory, and a related method is introduced for coarse-graining field-theoretic operators. The viability of this methodology is demonstrated by coarse-graining a field-theoretic model of a Gaussian-core fluid and thereby reducing lattice discretization errors.