A number of different methods have been used to attempt to ``accelerate'' the dynamics of Monte Carlo updates (i.e., reduce z).
The first two are commonly used to improve numerical solutions of PDEs.
In some cases, over-relaxation can reduce z to 
.
Multigrid Monte Carlo and Fourier acceleration work well in certain cases.
Cluster algorithms work very well, but currently are only
applicable to a small class of spin models.