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Exactly Solvable Lattice Models with Crossing Symmetry · Around

2012

Exactly Solvable Lattice Models with Crossing Symmetry

Simon, Steven H., Fendley, Paul

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We show how to compute the exact partition function for lattice statistical-mechanical models whose Boltzmann weights obey a special "crossing" symmetry.

The crossing symmetry equates partition functions on different trivalent graphs, allowing a transformation to a graph where the partition function is easily computed.
The simplest example is counting the number of nets without ends on the honeycomb lattice, including a weight per branching.
Other examples include an Ising model on the Kagome' lattice with three-spin interactions, dimers on any graph of corner-sharing triangles, and non-crossing loops on the honeycomb lattice, where multiple loops on each edge are allowed.

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