TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.2.029
TI  - Critical loop models are exactly solvable
PY  - 2024/08/01
UR  - https://scipost.org/SciPostPhys.17.2.029
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 2
SP  - 029
A1  - Nivesvivat, Rongvoram
AU  - Ribault, Sylvain
AU  - Jacobsen, Jesper Lykke
AB  - In two-dimensional critical loop models, including the O(n) and Potts models, the spectrum is exactly known, as are a few structure constants or ratios thereof. Using numerical conformal bootstrap methods, we study 235 of the simplest 4-point structure constants. For each structure constant, we find an analytic expression as a product of two factors: 1) a universal function of conformal dimensions, built from Barnes' double Gamma function, and 2) a polynomial function of loop weights, whose degree obeys a simple upper bound. We conjecture that all structure constants are of this form. For a few 4-point functions, we build corresponding observables in a lattice loop model. From numerical lattice results, we extract amplitude ratios that depend neither on the lattice size nor on the lattice coupling. These ratios agree with the corresponding ratios of 4-point structure constants.
ER  -

@Article{10.21468/SciPostPhys.17.2.029,
	title={{Critical loop models are exactly solvable}},
	author={Rongvoram Nivesvivat and Sylvain Ribault and Jesper Lykke Jacobsen},
	journal={SciPost Phys.},
	volume={17},
	pages={029},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.2.029},
	url={https://scipost.org/10.21468/SciPostPhys.17.2.029},
}