2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66745By adapting the renormalization techniques of Pisztora, we establish surface order large deviations estimates for FK-percolation on $\Z^2$ with parameter $q\geq 1$ 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.18 pages, 4 figuresProbability60F10; 60K35; 82B20; 82B43text