(a) A Hamilton path on a lattice and its associated list, in which sites are specified by their coordinates. The head of the path is site with coordinates . One of the nearest neighbors of is the site . A new path may be generated from the old one by reversing the order of the half-list lying above . (b) Another possible outcome occurs if we select the tail, , and its neighbor . Then we reverse the half-list lying below . After each maneuver, only a single edge has moved, but the end of the walk has jumped to a new lattice site.
Correlation “time” as a function of lattice size, or number of iterations needed to remove correlations between successive samples on lattices.
Correlation time in “real-time” units, or number of CPU seconds (on a Pentium III processor) needed to remove correlations between successive samples on lattices.
The three unique conformations of Hamilton paths on the lattice.
The quantity is the number of conformations on the lattice that appear times in samples. The symbols are results for the current algorithm, the solid curve is Eq. (1), the expected distribution assuming unbiased sampling.
The current algorithm has been shown to be rigorously ergodic, by exhaustive enumeration, on all the following lattices. represents the total number of unique Hamilton paths, counting any path and its reverse only once.
Performance statistics for the procedure on lattices of total size using a Pentium III processor. is defined as the CPU or real time required to complete iterations. is the correlation “time,” or a measure of the number of iterations needed to dissipate correlations between successive samples. is defined as the CPU or real time required to complete iterations.
Distributions of the different conformations obtained by three different sampling techniques. Rows one and two are taken from Ref. 10. Only the current algorithm samples the three conformations uniformly.
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