Department of Physics, Cornell University, Ithaca, NY 14853-2501, USA.
J Phys Condens Matter. 2011 Apr 27;23(16):164212. doi: 10.1088/0953-8984/23/16/164212. Epub 2011 Apr 6.
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.
我讨论了一组统计力学模型，其中有限群 G 的（某些类）元素占据格点的（有向）边；任何一个plaquette 上的乘积都被约束为群单位元 e。这样的模型可能具有拓扑序，即它的平衡系综具有不同的、对称相关的热力学分量，无法用任何局域序参量来区分。特别是，如果 G 是非阿贝尔群，拓扑序可能是非阿贝尔的。给出了特定模型的可行性标准，特别是对于蒙特卡罗更新。
