2009/10/23 by Christopher L. Henley, Henley, Christopher L. · 1 citation
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.0910.4574
17 pp, two figures. Massive revisions since 1st submission (one figure added, Sec VI transfer matrix added, total length 50% longer)
openalex publication_date 2009/10/23 · arxiv created 2011/03/18 · arxiv updated 2011/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.