Conjecture of an exact formula for 3-point functions of ℓ-leg and diagonal fields in critical loop models, supported by transfer-matrix numerics on cylinders that agree in most cases.
Bootstrap approach to geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: A study of the $s$-channel spectra
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abstract
We revisit in this paper the problem of connectivity correlations in the Fortuin-Kasteleyn cluster representation of the two-dimensional $Q$-state Potts model conformal field theory. In a recent work [M. Picco, S. Ribault and R. Santachiara, SciPost Phys. 1, 009 (2016); arXiv:1607.07224], results for the four-point functions were obtained, based on the bootstrap approach, combined with simple conjectures for the spectra in the different fusion channels. In this paper, we test these conjectures using lattice algebraic considerations combined with extensive numerical studies of correlations on infinite cylinders. We find that the spectra in the scaling limit are much richer than those proposed in [arXiv:1607.07224]: they involve in particular fields with conformal weight $h_{r,s}$ where $r$ is dense on the real axis.
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Three-point functions in critical loop models
Conjecture of an exact formula for 3-point functions of ℓ-leg and diagonal fields in critical loop models, supported by transfer-matrix numerics on cylinders that agree in most cases.