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Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator

By Marco Picco, Raoul Santachiara, Jacopo Viti and Gesualdo Delfino


22 pages, 6 figuresInternational audienceRecently, 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

Topics: [ PHYS.COND.CM-SM ] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th]
Publisher: Elsevier
Year: 2013
DOI identifier: 10.1016/j.nuclphysb.2013.07.014
OAI identifier: oai:HAL:hal-00818106v1
Provided by: Hal-Diderot
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