# Planar random-cluster model: scaling relations

@article{DuminilCopin2020PlanarRM, title={Planar random-cluster model: scaling relations}, author={Hugo Duminil-Copin and Ioan Manolescu}, journal={arXiv: Probability}, year={2020} }

This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4]$ using novel coupling techniques. More precisely, we derive the scaling relations between the critical exponents $\beta$, $\gamma$, $\delta$, $\eta$, $\nu$, $\zeta$ as well as $\alpha$ (when $\alpha\ge0$). As a key input, we show the stability of crossing probabilities in the near-critical regime using new interpretations of the notion of influence of an…

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