Convergence of Fermionic Observables in the Massive Planar FK-Ising Model

We prove convergence of the 2- and 4-point fermionic observables FK-Ising model on simply connected domains discretised by a planar isoradial lattice in massive (near-critical) scaling limit. The former is alternatively known as (fermionic) martingale observable (MO) for interface, particular encapsulates boundary visit probabilties interface. latter encodes connection probabilities alternating (generalised Dobrushin) condition, whose exact then further analysed to yield crossing estimates general conditions. Notably, we obtain version so-called Russo- Seymour-Welsh (RSW) type lattice. These satisfy s-holomorphicity [Smi10], develop robust techniques exploit this condition which do not require any regularity assumption domain or direction perturbation. Since many other near-critical same relation (cf. [BeDu12, CIM21, Par19]), these strategies are direct use analysis models broader setting.