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We have considered clusters of like spin in the Q-Potts model, the spin Pottsclusters. Using Monte Carlo simulations, we studied these clusters on a squarelattice with periodic boundary conditions for values of Q in [1,4]. We continuethe work initiated with Delfino and Viti (2013) by measuring the universalfinite size corrections of the two-point connectivity. The numerical data areperfectly compatible with the CFT prediction, thus supporting the existence ofa consistent CFT, still unknown, describing the connectivity Potts spinclusters. We provided in particular new insights on the energy field of suchtheory. For Q=2, we found a good agreement with the prediction that the Isingspin clusters behave as the Fortuin-Kasteleyn ones at the tri-critical point ofthe dilute 1-Potts model. We show that the structure constants are likely to begiven by the imaginary Liouville structure constants, consistently with theresults of Delfino et al. (2013) and of Ang and Sun (2021). For Q differentfrom 2 instead, the structure constants we measure do not correspond to anyknown bootstrap solutions. The validity of our analysis is backed up by themeasures of the spin Potts clusters wrapping probability for Q=3. We evaluatethe main critical exponents and the correction to the scaling. A new exact andcompact expression for the torus one-point of the Q-Potts energy field is alsogiven.

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