Dimers on surface graphs and spin structures. I

Abstract

Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures.

21 pages, 8 figures, minor modifications

References in corpus (1)

• Discrete Riemann Surfaces and the Ising model

Cited by in corpus (46)

• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Spin TQFTs and fermionic phases of matter
• Majorana Fermion Codes
• Dimers on surface graphs and spin structures. II
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases
• Simulation of rare events in quantum error correction
• The critical Z-invariant Ising model via dimers: locality property
• Anomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs
• A generalized Kac-Ward formula
• Self-Organized Criticality and Pattern Emergence through the lens of Tropical Geometry
• The combinatorial formula for open gravitational descendents
• Statistical physics through the lens of real-space mutual information
• The $Z$-invariant Ising model via dimers
• The critical Ising model via Kac-Ward matrices
• Disentangling interacting symmetry protected phases of fermions in two dimensions
• Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code
• Dimers on graphs in non-orientable surfaces
• Two-dimensional state sum models and spin structures
• Asymptotics of height change on toroidal Temperleyan dimer models
• Commuting-projector Hamiltonians for 2D topological insulators: edge physics and many-body invariants
• A tensor network approach to 2D bosonization
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• Geometric representation of binary codes and computation of weight enumerators
• Criticality and conformality in the random dimer model
• An Expansion Formula for Decorated Super-Teichmüller Spaces
• Geometric representations of linear codes
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Dimer Model: Full Asymptotic Expansion of the Partition Function
• Planar Graphical Models which are Easy
• Commuting projector models for (3+1)d topological superconductors via string net of (1+1)d topological superconductors
• Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants
• Dimer and fermionic formulations of a class of colouring problems
• Disordered Monomer-Dimer model on Cylinder graphs
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• Dimer geometry, amoebae and a vortex dimer model
• Identities between dimer partition functions on different surfaces
• The Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice
• A Pfaffian formula for the Ising partition function of surface graphs
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• 3D Quantum Gravity from Holomorphic Blocks
• Graph coverings and twisted operators
• The free-fermionic $C_2^{(1)}$ loop model, double dimers and Kashaev's recurrence
• Exactly Solvable Topological Phase Transition in a Quantum Dimer Model
• A Pfaffian formula for the monomer-dimer model on surface graphs