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Rotational invariance in critical planar lattice models

Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun, Ioan Manolescu, Mendes Oulamara

21/12/20 Published in : arXiv:2012.11672

In this paper, 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 from this result that the correlations of the Potts models with q\in\{2,3,4\} colors and of the six-vertex height function with \Delta\in[-1,-1/2] are rotationally invariant at large scales.

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  • Statistical Mechanics

Quantum Chern-Simons theories on cylinders: BV-BFV partition functions

On the six-vertex model's free energy

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