FIGURE 3.

Several indicators of proper sampling. (Left) The sampling of the F-H path ensemble represented as a tree. The x axis represent the time slices along each path, the y axis Monte Carlo simulation time. Starting with the initial path at the top, one shoots backward (left) and forward (right) in time. The solid vertical lines indicate the shooting points. Accepted (partial) paths are indicated in green (backward) and red (forward). While moving through the Monte Carlo time (downward), the entire path changes many times during the sampling. The thick blue line indicates the parts of the path ensemble that change the least. (Top right) Acceptance ratio for the F-H-path ensemble as a function of shooting-point time-slice index. The forward shooting is more accepted at the high end of the path, because it is already there in the basin of attraction of the H-state. The backward shooting is more accepted in the beginning of paths. Note that the simultaneous acceptance of both a forward and backward shot is extremely low, indicating the need for a stochastic algorithm. (Bottom right) Every 100th shooting attempt at a path, smoothed by running the averaging over 10 slices, is plotted in the (R_OH–Δ) plane. Every circle denotes a time slice. Groups of five subsequent paths are rendered in different colors to show that the sampling is reasonable. There is no apparent change in the ensemble over Monte Carlo simulation time (at least in this order parameter plane).