Classical height models with topological order

Details Classical height models with topological order Classical height models with topological order

2009-10-23

arxiv.org/abs/0910.4574v3

Physics

Condensed Matter

Statistical Mechanics

17 pp, two figures. Massive revisions since 1st submission (one figure added, Sec VI transfer matrix added, total length 50% l

Scientific paper

I discuss a family of statistical-mechanics models in which (some classes of) elements of a finite group $G$ occupy the (directed) edges of a lattice; the product around any plaquette is constrained to be the group identity $e$. Such a model may possess topological order, i.e. its equilibrium ensemble has distinct, symmetry-related thermodynamic components that cannot be distinguished by any local order parameter. In particular, if $G$ is a non-abelian group, the topological order may be non-abelian. Criteria are given for the viability of particular models, in particular for Monte Carlo updates.

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