%0 Journal Article %1 duminilcopin2020rotational %A Duminil-Copin, Hugo %A Kozlowski, Karol Kajetan %A Krachun, Dmitry %A Manolescu, Ioan %A Oulamara, Mendes %D 2020 %K %T Rotational invariance in critical planar lattice models %U http://arxiv.org/abs/2012.11672 %X 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 $1q4$ 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 $qın\2,3,4\$ colors and of the six-vertex height function with $\Deltaın-1,-1/2$ are rotationally invariant at large scales.

@article{duminilcopin2020rotational, abstract = {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.}, added-at = {2023-12-13T09:31:03.000+0100}, author = {Duminil-Copin, Hugo and Kozlowski, Karol Kajetan and Krachun, Dmitry and Manolescu, Ioan and Oulamara, Mendes}, biburl = {https://www.bibsonomy.org/bibtex/2f12b9e5ea6e4a563f046779c7ff0e4d8/admin}, interhash = {ceff696507ad8aaeb26bcb326f63d973}, intrahash = {f12b9e5ea6e4a563f046779c7ff0e4d8}, keywords = {}, note = {cite arxiv:2012.11672Comment: 92 pages, 29 pictures}, timestamp = {2023-12-13T09:31:03.000+0100}, title = {Rotational invariance in critical planar lattice models}, url = {http://arxiv.org/abs/2012.11672}, year = 2020 }