Bootstrap approach to geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: A study of the $s$-channel spectra

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.

70 pages, 12 figures. v2: Corrected affiliation

References in corpus (9)

• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• Logarithmic observables in critical percolation
• Correlation functions in loop models
• Phase diagram of the chromatic polynomial on a torus
• Eigenvalue amplitudes of the Potts model on a torus
• Combinatorial aspects of boundary loop models
• A fusion for the periodic Temperley-Lieb algebra and its continuum limit
• On the growth constant for square-lattice self-avoiding walks
• On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories

Cited by in corpus (4)

• Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• Four spins correlation function of the $q$ states Potts model, for general values of $q$. Its percolation model limit $q\to 1$
• Torus partition function of the six-vertex model from algebraic geometry