Abstract
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.
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He, Y., Grans-Samuelsson, L., Jacobsen, J.L. et al. Geometrical four-point functions in the two-dimensional critical Q-state Potts model: connections with the RSOS models. J. High Energ. Phys. 2020, 156 (2020). https://doi.org/10.1007/JHEP05(2020)156
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DOI: https://doi.org/10.1007/JHEP05(2020)156