Marco Picco, Raoul Santachiara, Jacopo Viti, Gesualdo Delfino
Recently, two of us argued that the probability that an FK cluster in the Q-state Potts model connects three given points is related to the time-like Liouville three-point correlation function. Moreover, they predicted that the FK three-point connectivity has a prefactor which unveils the effects of a discrete symmetry, reminiscent of the S_Q permutation symmetry of the Q=2,3,4 Potts model. Their theoretical prediction has been checked numerically for the case of percolation, corresponding to Q=1. We introduce the time-like Liouville correlator as the only consistent analytic continuation of the minimal model structure constants and present strong numerical tests of the relation between the time-like Liouville correlator and percolative properties of the FK clusters for real values of Q.
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http://arxiv.org/abs/1304.6511
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