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 by using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarsegrained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical coarse-graining schemes that are accompanied by a posteriori error estimates for lattice systems with short- and long-range interactions.
|Titolo:||Coarse-graining schemes for stochastic lattice systems with short and long-range interactions|
|Data di pubblicazione:||2014|
|Appare nelle tipologie:||1.1 Articolo in rivista|