Monte Carlo algorithms based on the number of potential moves

We discuss Monte Carlo dynamics based on [N(sigma, Delta E)](E), the (micro canonical) average number of potential moves which increase the energy by D elta E in a single spin Rip. The microcanonical average can be sampled usin g Monte Carlo dynamics of a single spin flip with a transition rate min(1, [N(sigma', E - E')](E')/[N(sigma, E' - E)](E)) from energy E to E'. A cumul ative average (over Monte Carte steps) can be used as a first approximation to the exact microcanonical average in the Rip rate. The associated histog ram is a constant independent of the energy. The canonical distribution of energy can be obtained from the transition matrix Monte Carlo dynamics. Thi s second dynamics has fast relaxation time - at the critical temperature th e relaxation time is proportional to specific heat. The dynamics are useful in connection with reweighting methods for computing thermodynamic quantit ies. (C) 2000 Elsevier Science B.V. All rights reserved.