Non-unitary observables in the 2d critical Ising model

Abstract

We introduce three non-local observables for the two-dimensional Ising model. At criticality, conformal field theory may be used to obtain theoretical predictions for their behavior. These formulae are explicit enough to show that their asymptotics are described by highest weights $h_{pq}$ from the Kac table for c=1/2 distinct from those of the three unitary representations (0, 1/16 and 1/2).

9 pages, 4 figures, Latex

References in corpus (3)

• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• Conformally Invariant Fractals and Potential Theory
• Crossing probabilities on same-spin clusters in the two-dimensional Ising model

Cited by in corpus (13)

• Logarithmic Minimal Models
• From Percolation to Logarithmic Conformal Field Theory
• Boundary Partitions in Trees and Dimers
• Logarithmic M(2,p) Minimal Models, their Logarithmic Couplings, and Duality
• Boundary algebras and Kac modules for logarithmic minimal models
• Frozen into stripes: fate of the critical Ising model after a quench
• A formula for crossing probabilities of critical systems inside polygons
• Exact logarithmic four-point functions in the critical two-dimensional Ising model
• Crossing Probabilities of Multiple Ising Interfaces
• Critical exponents for the homology of Fortuin-Kasteleyn clusters on a torus
• Using the Schramm-Loewner evolution to explain certain non-local observables in the 2d critical Ising model
• Schramm's formula for multiple loop-erased random walks
• Cluster densities at 2-D critical points in rectangular geometries