Integrable boundary Boltzmann weights and surface free energy inversion relations of the chiral Potts model |
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| Institution: | 1. Department of Mathematics, School of Mathematical Sciences, The Australian National University, Canberra ACT 0200, Australia;2. Institute of Modern Physics, Xiber University, Xian, China;1. Department of Aerospace Engineering, Tohoku University, 6-6-01, Aoba-yama, Aoba-ku, Sendai, Miyagi 980-8579, Japan;2. Institute of Fluid Science, Tohoku University, 2-2-1, Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan;3. Toray Composites (America), Inc., 19002 50th Avenue East, Tecoma, WA 98446, United States;4. Composite Materials Research Laboratories (CMRL), Toray Industries, Inc., Japan;1. Department of Applied Physics, Zhejiang University of Technology, Hangzhou, 310023, China;2. Department of Physics, Zhejiang University, Hangzhou, 310027, China;3. Institute of Bioinformatics and Medical Engineering, Jiangsu University of Technology, Changzhou, 213001, China;1. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), Departamento de Química, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CONICET – CC 16 Suc. 4, 1900, La Plata, Argentina;2. GSI Helmholtzzentrum für Schwerionenforschung, 64291, Darmstadt, Germany;3. Technische Universität Darmstadt, Materialwissenschaft, 64287, Darmstadt, Germany;1. Interdisciplinary Graduate Programme, Graduate College, Nanyang Technological University, Singapore, 637553, Singapore;2. Singapore Membrane Technology Centre, Nanyang Environment and Water Research Institute, Nanyang Technological University, Singapore, 637141, Singapore;3. School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, 639798, Singapore;4. School of Chemical and Biomedical Engineering, Nanyang Technological University, Singapore, 637459, Singapore;5. AGC Asia Pacific Pte Ltd, Singapore, 637143, Singapore |
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| Abstract: | The integrability of the chiral Potts model with boundaries is considered in this paper. The boundary star-triangle relation determining the boundary Boltzmann weights for the chiral Potts model is presented. By solving the boundary star-triangle relation the boundary Boltzmann weights are obtained. The fusion procedure is then applied to derive the functional relations of the transfer matrices of the model with boundaries. From these functional relations the inversion relations of the surface free energies are extracted when the system size is big enough. Surprisingly, the inversion relation of the local surface free energy is as simple as those of other non-chiral models, but it has still to be solved. |
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