This applet simulates a dimer model on the square lattice. Each dimer is allowed to slide along its axis, but with a hard-core constraint, so that it can only slide into a hole (monomer). The model can be defined with any number of monomers, but in we our paper, and for this applet, we look only generate single-monomer states. Intstructions for using the applet appear below the applet.
As discussed in the paper, these systems have a weak localization behavior that can be understood by a mapping to spanning webs. Click here for an applet simulating spanning webs.
We have also done similar work studying dimers on a triangular lattice.
Click on the "Randomize" button to create a random state with the desired system size.
Click on the "Step Forward" button to run the system forward. With a "1" in the field to the left of the button, one dimer will be moved at random (if possible). To make more than one move, just change the number in the field to the left of the button.
Dimers that have never moved are colored green. Dimer moved immediately after clicking the "Step Forward" button are colored red, while all other dimers have have moved at some point in the course of the simulation are colored blue.
The first field in the bottom right gives the number of sites with have not had a dimer move on, off, or over them, since the simulation began. The second one tells how many dimer moves have occurred.
You can decide whether or not you want to display the underlying monomer tree. "Monomer trees" are defined in the paper. If you show trees, the sites that are accessible to the monomer (after waiting arbitrarily long amounts of time) are colored pink. One of the key results in the paper is that single monomers are weakly localized---for an infinite system, the number of sites that a monomer can reach is always finite, but follows a power law distribution with an infinite average. (For a finite system, you will sometimes see that every site is marked pink, which means that the monomer can reach every site; this happens with zero probability in the infinite system limit.)