POSSIBLE BARRIER AT Z-APPROXIMATE-TO-1 FOR LOCAL ALGORITHMS

It is shown that a certain class of generalizations of overrelaxation algorithms is incapable of further reducing the dynamical exponent z below its standard overrelaxed value of z almost-equal-to 1. The mean-field value is unity and is obtained in a theory that is free in the static limit, while the effect of interactions and dimensionality could be estimated with dynamical renormalization-group methods. The generalizations are obtained by viewing overrelaxation as a slightly deformed deterministic algorithm and should, therefore, hold for hybrid Monte Carlo algorithms as well.