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 (Delfino and Viti, 2011) [1]. 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. We revisit the derivation of the time-like Liouville correlator (Zamolodchikov, 2005) [2] and show that this is the only consistent analytic continuation of the minimal model structure constants. We then 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. (C) 2013 Elsevier B.V. All rights reserved.

Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator / Picco, M; Santachiara, R; Viti, J; Delfino, Gesualdo. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - 875:3(2013), pp. 719-737. [10.1016/j.nuclphysb.2013.07.014]

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

Delfino, Gesualdo
2013

Abstract

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 (Delfino and Viti, 2011) [1]. 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. We revisit the derivation of the time-like Liouville correlator (Zamolodchikov, 2005) [2] and show that this is the only consistent analytic continuation of the minimal model structure constants. We then 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. (C) 2013 Elsevier B.V. All rights reserved.
875
3
719
737
https://arxiv.org/abs/1304.6511
Picco, M; Santachiara, R; Viti, J; Delfino, Gesualdo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/11807
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