On the CFT describing the spin clusters in 2d Potts model

We have considered clusters of like spin in the Q-Potts model, Potts clusters. Using Monte Carlo simulations, we studied these on a square lattice with periodic boundary conditions for values Q [1,4]. continue work initiated Delfino and Viti (2013) by measuring universal finite size corrections two-point connectivity. The numerical data are perfectly compatible CFT prediction, thus supporting existence consistent CFT, still unknown, describing connectivity provided particular new insights energy field such theory. For Q=2, found good agreement prediction that Ising behave as Fortuin-Kasteleyn ones at tri-critical point dilute 1-Potts model. show structure constants likely to be given imaginary Liouville constants, consistently results et al. Ang Sun (2021). different from 2 instead, measure do not correspond any known bootstrap solutions. validity our analysis is backed up measures wrapping probability Q=3. evaluate main critical exponents correction scaling. A exact compact expression torus one-point also given.