Rotational invariance in critical planar lattice models

Understand

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.