Dimers on graphs in non-orientable surfaces

Abstract

The main result of this paper is a Pfaffian formula for the partition function of the dimer model on a graph G embedded in a closed, possibly non-orientable surface S. This formula is suitable for computational purposes, and it is obtained using purely geometrical methods. The key step in the proof consists of a correspondence between some orientations on G and the set of pin^- structures on S. This generalizes (and simplifies) the results of a previous paper [2].

27 pages, 5 figures; minor changes in v3

References in corpus (2)

• Discrete Riemann Surfaces and the Ising model
• Dimers on surface graphs and spin structures. I

Cited by in corpus (10)

• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Anomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs
• A generalized Kac-Ward formula
• Duality between Spin networks and the 2D Ising model
• Commuting-projector Hamiltonians for 2D topological insulators: edge physics and many-body invariants
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• Identities between dimer partition functions on different surfaces
• A Pfaffian formula for the Ising partition function of surface graphs
• Graph coverings and twisted operators
• A Pfaffian formula for the monomer-dimer model on surface graphs