Universal amplitude ratios in the two-dimensional \(q\)-state Potts model and percolation from quantum field theory. (English) Zbl 0949.82008
Summary: We consider the scaling limit of the two-dimensional \(q\)-state Potts model for \(q\leqslant 4\). We use the exact scattering theory proposed by Chim and Zamolodchikov to determine the one- and two-kink form factors of the energy, order and disorder operators in the model. Correlation functions and universal combinations of critical amplitudes are then computed within the two-kink approximation in the form factor approach. Very good agreement is found whenever comparison with exact results is possible. We finally consider the limit \(q\rightarrow 1\) which is related to the isotropic percolation problem. Although this case presents a serious technical difficulty, we predict a value close to 74 for the ratio of the mean cluster size amplitudes above and below the percolation threshold. Previous estimates for this quantity range from 14 to 220.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 82B23 | Exactly solvable models; Bethe ansatz |
| 81T25 | Quantum field theory on lattices |
| 82B43 | Percolation |
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