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

A bstract 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.