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

TL;DR

This paper introduces coarse-graining methods for stochastic lattice models with both short- and long-range interactions, analyzing their accuracy and developing semi-analytical schemes with error estimates.

Contribution

It presents a novel hierarchical approach to coarse-graining for complex lattice systems, including error quantification and correction terms.

Findings

Effective coarse-graining schemes for mixed interaction ranges

Quantitative error bounds for approximations

Hierarchical correction terms improve accuracy

Abstract

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.