11 research outputs found
Cluster Hybrid Monte Carlo Simulation Algorithms
We show that addition of Metropolis single spin-flips to the Wolff cluster
flipping Monte Carlo procedure leads to a dramatic {\bf increase} in
performance for the spin-1/2 Ising model. We also show that adding Wolff
cluster flipping to the Metropolis or heat bath algorithms in systems where
just cluster flipping is not immediately obvious (such as the spin-3/2 Ising
model) can substantially {\bf reduce} the statistical errors of the
simulations. A further advantage of these methods is that systematic errors
introduced by the use of imperfect random number generation may be largely
healed by hybridizing single spin-flips with cluster flipping.Comment: 16 pages, 10 figure
New Lower Bounds on the Self-Avoiding-Walk Connective Constant
We give an elementary new method for obtaining rigorous lower bounds on the
connective constant for self-avoiding walks on the hypercubic lattice .
The method is based on loop erasure and restoration, and does not require exact
enumeration data. Our bounds are best for high , and in fact agree with the
first four terms of the expansion for the connective constant. The bounds
are the best to date for dimensions , but do not produce good results
in two dimensions. For , respectively, our lower bound is within
2.4\%, 0.43\%, 0.12\%, 0.044\% of the value estimated by series extrapolation.Comment: 35 pages, 388480 bytes Postscript, NYU-TH-93/02/0