Holomorphic Spinor Observables in the Critical Ising Model

Abstract

We introduce a new version of discrete holomorphic observables for the critical planar Ising model. These observables are holomorphic spinors defined on double covers of the original multiply connected domain. We compute their scaling limits, and show their relation to the ratios of spin correlations, thus providing a rigorous proof to a number of formulae for those ratios predicted by CFT arguments.

Significantly revised version (29 pages, 4 figures): the introduction is rewritten, the main convergence theorem is divided into two (Theorems 3.13 and 3.16 now), several improvements and rearrangements are made in Sections 3 and 4, the results of Section 5 are written in a slightly greater generality

References in corpus (4)

• Spanning forests and the vector bundle Laplacian
• Conformal Invariance of Spin Correlations in the Planar Ising Model
• The energy density in the planar Ising model
• Conformal invariance of loops in the double-dimer model

Cited by in corpus (1)

• Ising Model Observables and Non-Backtracking Walks