Lucas D'Alimonte

Analyticity of the correlation length in subcritical FK-percolation and Potts models

We prove that the correlation length of FK-percolation and Potts models on $\mathbb{Z}^d$ is analytic in the whole subcritical regime of parameters. Our proof makes use of the identification of the polar dual of the mass with the solution of an equation involving the leading eigenvalue of the FK--Ruelle operator, intro...