Renormalization multigrid (RMG): Statistically optimal renormalization group flow and coarse-to-fine Monte Carlo acceleration

Authors
Citation
A. Brandt et D. Ron, Renormalization multigrid (RMG): Statistically optimal renormalization group flow and coarse-to-fine Monte Carlo acceleration, J STAT PHYS, 102(1-2), 2001, pp. 231-257
Citations number
19
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
JOURNAL OF STATISTICAL PHYSICS
ISSN journal
0022-4715 → ACNP
Volume
102
Issue
1-2
Year of publication
2001
Pages
231 - 257
Database
ISI
SICI code
0022-4715(200101)102:1-2<231:RM(SOR>2.0.ZU;2-A
Abstract
New renormalization-group algorithms are developed with adaptive representa tions of the renormalized system which automatically express only significa nt interactions. As the amount of statistics grows, more interactions enter , thereby systematically reducing the truncation error. This allows statist ically optimal calculation of thermodynamic limits, in the sense that it ac hieves accuracy epsilon in just O(epsilon (-2)) random number generations. There are practically no finite-size effects and the renormalization transf ormation can be repeated arbitrarily many times. Consequently. the desired fixed point is obtained and the correlation-length critical exponent nu is extracted. In addition, we introduce a new multiscale coarse-to-fine accele ration method, based on a multigrid-like approach. This general (non-cluste r) algorithm generates independent equilibrium configurations without slow down. A particularly simple version of it can be used at criticality. The m ethods are of great generality; here they are demonstrated on the 2D Ising model.