Coarse-graining schemes for stochastic lattice systems with short and long-range interactions

Details Coarse-graining schemes for stochastic lattice systems with short and long-range interactions Coarse-graining schemes for stochastic lattice systems with short and long-range interactions

2010-03-07

arxiv.org/abs/1003.1506v1

Mathematics

Numerical Analysis

31 pages, 2 figures

Scientific paper

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.

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