MULTIBODY INTERACTIONS IN COARSE-GRAINING SCHEMES FOR EXTENDED SYSTEMS

Publication Date

2008

Journal or Book Title

SIAM JOURNAL ON SCIENTIFIC COMPUTING

Abstract

In this paper we address the role of multibody interactions for the coarse-grained approximation of stochastic lattice systems. Such interaction potentials are often not included in coarse-graining schemes, as they can be computationally expensive. The multibody interactions are obtained from the error expansion of the reference measure which is, in many cases, chosen as a Gibbs measure corresponding to a local mean-field approximation. We identify the parameter $\epsilon$ that characterizes the level of approximation and its relation to the underlying interaction potential. The error analysis suggests strategies to overcome the computational costs due to evaluations of multibody interactions by additional approximation steps with controlled errors. We present numerical examples demonstrating that the inclusion of multibody interactions shows substantial improvement in dynamical simulations, e.g., of rare events and metastability in phase transitions regimes.

Comments

The published version is located at http://epubs.siam.org/sisc/resource/1/sjoce3/v31/i2/p987_s1

Pages

987-1015

Volume

31

Issue

2

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