Surface order large deviations for 2D FK-percolation and Potts models (Q2485784)

The authors derive surface large deviations estimates for Bernoulli percolation, for FK-percola\-tion with parameter \(q\geq 1\) and for the corresponding Potts models on the planar lattice \(Z^2\). The result concerns asymptotics of FK-measures on finite boxes \(B(n)=(-n/2,n/2]^2 \cap Z^2\) and states that up to large deviations of surface order, there exists a unique biggest cluster in the box \(B(n)\) with the same density as the infinite cluster, and that the set of clusters of intermediate size has a negligible volume.