Journal article

Conformal Invariance of Spin Pattern Probabilities in the Planar Ising Model

We study the 2-dimensional Ising model at critical temperature on a smooth simply-connected graph Ω.We rigorously prove the conformal invariance of arbitrary spin-pattern probabilities centered at a point a and derive formulas to compute the probabilities as functions of the conformal map from Ω to the unit disk. Our methods extend those of [Hon10] and [CHI13] which proved conformal invariance of energy densities and spin correlations for points fixed far apart from each other. We use discrete complex analysis techniques and construct a discrete multipoint fermionic observable that takes values related to pattern probabilities in the planar Ising model. Refined analysis of the convergence of the discrete observable to a continuous, conformally covariant function completes the result.


    • EPFL-ARTICLE-200331

    Record created on 2014-07-21, modified on 2016-08-09

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