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In a recent paper "Ising Disks: topology preserving glauber dynamics" (w. Yuliy Baryshnikov), we introduced a Glauber dynamics on a subset of contractible cubical complexes, which we call clumps (see Pach's animals for a related definition). In the planar special case, where the state space is equivalent to the set of self-avoiding polygons, some illustrations are below.
In a recent paper "Ising Disks: topology preserving glauber dynamics" (w. Yuliy Baryshnikov), we introduced a Glauber dynamics on a subset of contractible cubical complexes, which we call clumps (see Pach's animals for a related definition). In the planar special case, where the state space is equivalent to the set of self-avoiding polygons, some illustrations are below.
Super critical regime where birth/death ratio is too high. The clump is growing indefinitely and looks like a ball, except some cracks.
Super Critical.mp4Below, the birth/death ratio is still higher than the critical value, so it still grows indefinitely but it is low enough that the clump grows much more branchy than a ball.
Above criticality.mp4Below, the growth rate is too small to sustain indefinite growth, so the clump stays bounded. The Markov chain is ergodic.
Below Criticality.mp4Page updated
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