Article
Multibody interactions in coarse-graining schemes for extended systems
SIAM Journal on Scientific Computing (2008)
• , University of Massachusetts - Amherst
• , University of Massachusetts - Amherst
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.
Keywords
• coarse-graining,
• relative entropy,
• lattice spin systems,
• Monte Carlo method,
• Gibbs measure,
• cluster expansion,
• multibody interactions,
• renormalization group map
Disciplines
Publication Date
2008
Publisher Statement
DOI: 10.1137/080713276
Citation Information
S Are, MA Katsoulakis, P Plechac and L Rey-Bellet. "Multibody interactions in coarse-graining schemes for extended systems" SIAM Journal on Scientific Computing Vol. 31 Iss. 2 (2008)
Available at: http://works.bepress.com/luc_rey_bellet/4/