For two new models in which occupied sites draw line segments to their nearest occupied neighbors, the paper proves that infinite connected clusters exist for sparse sites and do not exist for dense sites, and it establishes partial bounds on the independent model's phase boundary.
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Alignment percolation
For two new models in which occupied sites draw line segments to their nearest occupied neighbors, the paper proves that infinite connected clusters exist for sparse sites and do not exist for dense sites, and it establishes partial bounds on the independent model's phase boundary.