Conformal invariance of lattice models
arXiv:1109.1549
Abstract
These lecture notes provide a (almost) self-contained account on conformal invariance of the planar critical Ising and FK-Ising models. They present the theory of discrete holomorphic functions and its applications to planar statistical physics (more precisely to the convergence of fermionic observables). Convergence to SLE is discussed briefly. Many open questions are included.
70 pages, 19 figures
References in corpus (2)
Cited by in corpus (21)
- Topological Defects on the Lattice: Dualities and Degeneracies
- Parafermionic conformal field theory on the lattice
- A solution space for a system of null-state partial differential equations 3
- Conformal invariance of boundary touching loops of FK Ising model
- The near-critical planar FK-Ising model
- Percolation since Saint-Flour
- A formula for crossing probabilities of critical systems inside polygons
- Towards a conformal field theory for Schramm-Loewner evolutions
- Discrete holomorphicity and integrability in loop models with open boundaries
- Energy correlations of non-integrable Ising models: The scaling limit in the cylinder
- Integrability as a consequence of discrete holomorphicity: the Z_N model
- Theta-point polymers in the plane and Schramm-Loewner evolution
- Bridges in the random-cluster model
- The Ultraviolet Structure of Quantum Field Theories. Part 2: What is Quantum Field Theory?
- Multiple-SLE connectivity weights for rectangles, hexagons, and octagons
- q-deformed Loewner evolution
- Tensor Field Theories: Renormalization and Random Geometry
- Conformal Field Theory, Vertex Operator Algebra and Stochastic Loewner Evolution in Ising Model
- Renormalization of crossing probabilities in the dilute Potts model
- Feynman checkers: through the looking-glass
- Self-avoiding walk on with Yang-Baxter weights: universality of critical fugacity and 2-point function