Universal amplitude ratios in the two-dimensional q-state Potts model and percolation from quantum field theory |
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Institution: | 1. Graduate School of Medicine and Engineering, University of Yamanashi, Takeda 4-3-11, Kofu 400-8511, Japan;2. Faculty of Science and Technology, Seikei University, Kitamachi 3-3-1, Musashino, Tokyo 180-8633, Japan |
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Abstract: | We consider the scaling limit of the two-dimensional q-state Potts model for q ⩽ 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 → 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. |
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