  We study transition matrices for projected dynamics in the
energy-magnetization space, magnetization space and energy space. Several
single spin flip dynamics are considered such as the Glauber and Metropolis
canonical ensemble dynamics and the Metropolis dynamics for three
multicanonical ensembles: the flat energy-magnetization histogram, the flat
energy histogram and the flat magnetization histogram. From the numerical
diagonalization of the matrices for the projected dynamics we obtain the
sub-dominant eigenvalue and the largest relaxation times for systems of varying
size. Although, the projected dynamics is an approximation to the full state
space dynamics comparison with some available results, obtained by other
authors, shows that projection in the magnetization space is a reasonably
accurate method to study the scaling of relaxation times with system size. The
transition matrices for arbitrary single-spin flip dynamics are obtained from a
single Monte-Carlo estimate of the infinite temperature transition-matrix, for
each system size, which makes the method an efficient tool to evaluate the
relative performance of any arbitrary local spin-flip dynamics. We also present
new results for appropriately defined average tunnelling times of magnetization
and compute their finite-size scaling exponents that we compare with results of
energy tunnelling exponents available for the flat energy histogram
multicanonical ensemble.

Statistical Mechanics