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

By adapting the renormalization techniques of Pisztora (Probab. Theory Relat. Fields 104 (1996) 427), we establish surface order large deviations estimates for FK-percolation on with parameter q[greater-or-equal, slanted]1 and for the corresponding Potts models. Our results are valid up to the exponential decay threshold of dual connectivities which is widely believed to agree with the critical point.