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Plaquettes, spheres, and entanglement. (English) Zbl 1229.60107
The authors consider the plaquette percolation model, that is a natural dual to bond percolation in two and more dimensions, and prove that the high-density plaquette percolation model in \(d\) dimensions contains a surface that is homeomorphic to the \((d-1)\)-sphere and encloses the origin. This is proved by a path-counting argument in a dual bond percolation model.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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