To decorrelate a configuration, need to make changes on a scale **>**
spatial correlation length. For ** local** MC
algorithms (such as Metropolis) the effect of a change is only seen by nearest
neighbors. Since the update is a stochastic process, the changes should
propagate through the system like a random walk, so the number
of iterations required to propagate a distance goes like .
At the critical point, , so we expect .
This is a major problem for MC simulations, since we need large **L**.

More generally, where **z** is called the * dynamic
critical exponent*.
For a local algorithm and usually .
One of the active areas of research in MC simulation is
trying to find new algorithms with **z<2**.
These are usually non-local, multi-scale algorithms,
c.f. multigrid methods for solving PDEs,
where the same type of problem occurs.

Paul Coddington, Northeast Parallel Architectures Center at Syracuse University, paulc@npac.syr.edu