We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a d-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states and using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical schemes that are accompanied with a posteriori error estimates for coarse-grained lattice systems with short and long-range interactions.
Katsoulakis, MA; Plechac, P; Rey-Bellet, L; and Tsagkarogiannis, D, "COARSE-GRAINING SCHEMES FOR STOCHASTIC LATTICE SYSTEMS WITH SHORT AND LONG-RANGE INTERACTIONS" (2010). Mathematics and Statistics Department Faculty Publication Series. 1184.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1184