The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912601886162944 |
|---|---|
| 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 |