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
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.