Simulation of a critical state without critical slowing down by a renormalization group multi-grid method

We have implemented and tested a method to eliminate critical slowing down from Monte Carlo (and possibly other) simulations of very large systems, even for a “critical” state, where the correlation length of fluctuations is the size of the sample. Static correlation functions on all length scales (down to microscopic!) may thus be obtained with an amount of work asymptotically growing with size only as in conventional simulations of nearly uncorrelated states. In the simulation we use a finite but large set of approximated renormalized coupling constants, which describe very closely the coarse grained variable interactions of the simulated model. As a test bed, the 2D Ising model has been used. The method has the advantage that critical states of other types of systems can be simulated along the same line.