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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.03259 |
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| _version_ | 1866912601886162944 |
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| author | Duits, Maurice Hayford, Nathan Lee, Seung-Yeop |
| author_facet | Duits, Maurice Hayford, Nathan Lee, Seung-Yeop |
| contents | 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 is consistent with the predictions of Kazakov and Boulatov on this model, as well as subsequent confirmation of this formula using combinatorial methods. We also provide a new parametric formula for the free energy and give a characterization of the phase space. Our analysis is based on a steepest descent Riemann-Hilbert analysis of the associated biorthogonal polynomials and the corresponding isomonodromic $τ$-function. A key ingredient in the analysis is a parametrization of the spectral curve. This analysis lays the groundwork for the subsequent study of the multicritical point, which we will study in a forthcoming work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function Duits, Maurice Hayford, Nathan Lee, Seung-Yeop Mathematical Physics 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 is consistent with the predictions of Kazakov and Boulatov on this model, as well as subsequent confirmation of this formula using combinatorial methods. We also provide a new parametric formula for the free energy and give a characterization of the phase space. Our analysis is based on a steepest descent Riemann-Hilbert analysis of the associated biorthogonal polynomials and the corresponding isomonodromic $τ$-function. A key ingredient in the analysis is a parametrization of the spectral curve. This analysis lays the groundwork for the subsequent study of the multicritical point, which we will study in a forthcoming work. |
| title | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2405.03259 |