The \(Z\)-Dirac and massive Laplacian operators in the \(Z\)-invariant Ising model

DOI10.1214/21-EJP601zbMath1469.82007arXiv1801.00207MaRDI QIDQ2042876

Béatrice de Tilière

Publication date: 21 July 2021

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.00207

zbMATH Keywords

Ising modeldimer model\(Z\)-invariancediscrete massive harmonic and holomorphic functionsmassive Laplacian and Dirac operatorsspanning forests and spanning trees

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Elliptic functions and integrals (33E05)

Related Items (max. 100)

Elliptic dimers on minimal graphs and genus 1 Harnack curves ⋮ Universality of spin correlations in the Ising model on isoradial graphs ⋮ Minimal bipartite dimers and higher genus Harnack curves ⋮ Convergence of fermionic observables in the massive planar FK-Ising model

Cites Work

• Critical Ising model and spanning trees partition functions
• The critical temperature for the Ising model on planar doubly periodic graphs
• Universality in the 2D Ising model and conformal invariance of fermionic observables
• The fermionic observable in the Ising model and the inverse Kac-Ward operator
• The \(Z\)-invariant massive Laplacian on isoradial graphs
• Conformal invariance in random cluster models. I: Holomorphic fermions in the Ising model
• The critical \(Z\)-invariant Ising model via dimers: Locality property
• Discrete complex analysis on isoradial graphs
• Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances
• Smirnov's fermionic observable away from criticality
• Height representation of XOR-Ising loops via bipartite dimers
• Quadri-tilings of the plane
• The critical \(Z\)-invariant Ising model via dimers: the periodic case
• Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas
• An exploration of the permanent-determinant method
• Local statistics of lattice dimers
• The Laplacian and Dirac operators on critical planar graphs
• Critical temperature of periodic Ising models
• The height fluctuations of an off-critical dimer model on the square grid
• Elliptic functions and applications
• From cycle rooted spanning forests to the critical Ising model: an explicit construction
• Trees and matchings
• Kac-Ward operators, Kasteleyn operators, and \(s\)-holomorphicity on arbitrary surface graphs
• Revisiting the combinatorics of the 2D Ising model
• Determinantal spanning forests on planar graphs
• Dimers and amoebae
• A variational principle for domino tilings
• The statistics of dimers on a lattice
• Off-critical lattice models and massive SLEs
• Discrete Complex Analysis and Probability
• Rhombic embeddings of planar quad-graphs
• Dimer problem in statistical mechanics-an exact result
• Dimer geometry, amoebae and a vortex dimer model
• Dimers and cluster integrable systems
• Towards conformal invariance of 2D lattice models
• Potential theory on a rhombic lattice
• Statistics of the Two-Dimensional Ferromagnet. Part I
• Statistics of the Two-Dimensional Ferromagnet. Part II
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Discrete Riemann surfaces and the Ising model.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The \(Z\)-Dirac and massive Laplacian operators in the \(Z\)-invariant Ising model