Geometrical four-point functions in the two-dimensional critical Q-state Potts model: connections with the RSOS models

Yifei He (1) , Linnea Grans-Samuelsson (1) , Jesper Lykke Jacobsen (1, 2) , Hubert Saleur (1, 3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 Champs Aléatoires et Systèmes hors d'Équilibre
3 USC - University of Southern California

The “bootstrap determination” of the geometrical correlation functions in the two-dimensional Potts model proposed in a paper by Picco et al. [1] was later shown in [2] to be incorrect, the actual spectrum of the model being considerably more complex than initially conjectured. We provide in this paper a geometrical interpretation of the four- point functions built in [1], and explain why the results obtained by these authors, albeit incorrect, appeared so close to those of their numerical simulations of the Potts model. Our strategy is based on a cluster expansion of correlation functions in RSOS minimal models, and a subsequent numerical and algebraic analysis of the corresponding s-channel spectrum, in full analogy with our early work on the Potts model [2]. Remarkable properties of the lattice amplitudes are uncovered, which explain in particular the truncation of the spectrum of [2] to the much simpler one of the RSOS models, and which will be used in a forthcoming paper to finally determine the geometrical four-point functions of the Potts model itself.

Mots clés: Conformal Field Theory; Field Theories in Lower Dimensions; Lattice Integrable Models; n-point function: 4; Potts model; dimension: 2; expansion: cluster; model: minimal; algebra: Temperley-Lieb; partition function; bootstrap; numerical calculations

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]; Physique Générale [physics.gen-ph]

Yifei He, Linnea Grans-Samuelsson, Jesper Lykke Jacobsen, Hubert Saleur. Geometrical four-point functions in the two-dimensional critical Q-state Potts model: connections with the RSOS models. Journal of High Energy Physics, 2020, 2020 (5), pp.156. ⟨10.1007/JHEP05(2020)156⟩. ⟨hal-02504616⟩