Coarse-graining schemes for stochastic lattice systems with short and long-range interactions.
This work addresses the challenge of efficiently simulating many-particle systems with competing interactions, offering rigorous error control for coarse-grained models.
The paper develops coarse-graining schemes for stochastic lattice systems with short- and long-range interactions, providing a hierarchy of correction terms and semi-analytical numerical schemes with a posteriori error estimates.
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.