Diamond Ice

摘要

The bounded version of the ice model of statistical mechanics is studied. We consider it in a diamond domain on the Z~2-lattice. The configurations sharing a boundary configuration are shown to be connected under simple loop perturbations. This enables an efficient generation of the configurations with a probabilistic cellular automaton. The fill-in from the boundary is critically dependent on the values of the height function along the boundary. We characterize the phenomena at the extrema of this function as well as in some highly nontrivial cases where results analogous to and more complex than the Arctic Circle Theorem for dominoes hold.