UNIVERSAL AMPLITUDE RATIOS IN THE 2-DIMENSIONAL Q-STATE POTTS-MODEL AND PERCOLATION FROM QUANTUM-FIELD THEORY

We consider the scaling limit of the two-dimensional q-state Potts mod el for q less than or equal to 4. We use the exact scattering theory p roposed by Chim and Zamolodchikov to determine the one- and two-kink f orm factors of the energy, order and disorder operators in the model. Correlation functions and universal combinations of critical amplitude s are then computed within the two-kink approximation in the form fact or approach. Very good agreement is found whenever comparison with exa ct results is possible. We finally consider the limit q --> 1 which is related to the isotropic percolation problem. Although this case pres ents a serious technical difficulty, we predict a value close to 74 fo r the ratio of the mean cluster size amplitudes above and below the pe rcolation threshold. Previous estimates for this quantity range from 1 4 to 220. (C) 1998 Elsevier Science B.V.