  We propose a new local algorithm for the thermalization of n-vector spin
models, which can also be used in the numerical simulation of SU(N) lattice
gauge theories. The algorithm combines heat-bath (HB) and micro-canonical
updates in a single step -- as opposed to the hybrid overrelaxation method,
which alternates between the two kinds of update steps -- while preserving
ergodicity. We test our proposed algorithm in the case of the one-dimensional
4-vector spin model and compare its performance with the standard HB algorithm
and with other HB-inspired algorithms.
