The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function
| Autor: | Duits, Maurice, Hayford, Nathan, Lee, Seung-Yeop |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We compute the genus $0$ free energy for the $2$-matrix model with quartic interactions, which acts as a generating function for the Ising model's partition function on a random, $4$-regular, planar graph. This rigorously confirms the predictions of V.A. Kazakov and D.V. Boulatov on this model, and provides a new parametric formula for the free energy. We also give a characterization of the phase space of the model. Our analysis is based on a steepest descent Riemann-Hilbert analysis of the associated biorthogonal polynomials and the corresponding isomonodromic $\tau$-function. A key ingredient in the analysis is a parametrization of the spectral curve. Comment: Version 1: 83 pages, 17 figures. Comments welcome! |
| Databáze: | arXiv |
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