Exact sampling from non-attractive distributions using summary states
Warning: some of the pictures are rather reminiscent of Reservoir
These animations show the summary state method in action for an Ising model
on a periodic triangular lattice. Black and white indicate up and down
spins, and red indicates an uncertain spin (i.e., ?).
Note that in ferromagnetic cases, the animation is the same as it would be
using the Propp and Wilson algorithm, with red indicating spins that differ
between the bounding states. The antiferromagnetic case is non-attractive,
and hence is beyond the scope of the original Propp and Wilson algorithm.
The following animations show the effect of introducing a single uncertain
spin into a nearly equilibrated lattice of an antiferromagnetic Ising
system. Spins were set up or down with equal probability, and the system
was simulated forward in time for 100 iterations. Then a randomly chosen
made uncertain, and the simulation was continued.
Each frame shows the
result of one iteration, which involves updating every spin in the lattice.
Note that the threshold for convergence of the algorithm is T=4.83.
Note: The delay between frames is set short, so if the animations seem
to run sluggishly, you may want to download them to a
local machine and then view them.
Last modified: Mon May 8 11:04:13 2000