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Rotational invariance in critical planar lattice models

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arxiv 2012.11672 v2 pith:S4EZGZVW submitted 2020-12-21 math.PR math-phmath.MPnlin.SI

Hugo Duminil-Copin , Karol Kajetan Kozlowski , Dmitry Krachun , Ioan Manolescu , Mendes Oulamara This is my paper
classification math.PRmath-phmath.MPnlin.SI
keywords latticemodelscriticalinvarianceinvariantlargemodelprove
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abstract

We prove that the large-scale properties of a number of two-dimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the square lattice with cluster-weight $1\le q\le 4$ exhibits rotational invariance at large scales. This covers the case of Bernoulli percolation on the square lattice as an important example. We deduce that the correlations of the critical Potts models with $q\in\{2,3,4\}$ colours are rotationally invariant at large scales. Our result is instrumental in proving the convergence of the six-vertex model to the Gaussian Free Field in a separate paper.

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Cited by 4 Pith papers

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