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Curvature matrix models for dynamical triangulations and the Itzykson-Di Francesco formula |
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| Institution: | 1. College of Information & Engineering, Wenzhou Medical University, Wenzhou 325035, PR China;2. Department of Automatics and Applied Informatics, Aurel Vlaicu University of Arad, Arad 310095, Romania;3. Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, FL 32825, USA;1. Department of Physics, Laboratory of Computational Materials Physics, Jiangxi Normal University, Nanchang 330022, China;2. College of Chemistry and Chemical Engineering, Hubei Key Laboratory for Processing and Application of Catalytic Materials, Huanggang Normal University, Huanggang 438000, China;3. School of Science, Nanchang Institute of Technology, Nanchang 330099, China |
| Abstract: | We study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the model can be solved by resumming the Itzykson-Di Francesco formula over congruence classes of Young tableau weights modulo three. From this we show that the large-N limit implies a non-trivial correspondence with models of random surfaces weighted with only even coordination number vertices. We examine the critical behaviour and evaluation of observables and discuss their interrelationships in all models. We obtain explicit solutions of the model for simple choices of vertex weightings and use them to show how the matrix model reproduces features of the random surface sum. We also discuss some general properties of large-N character expansion approach as well as potential physical applications of our results. |
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