The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function
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 subse...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2025 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2025
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214089 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function. Maurice Duits, Nathan Hayford and Seung-Yeop Lee. SIGMA 21 (2025), 079, 90 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862637764014505984 |
|---|---|
| author | Duits, Maurice Hayford, Nathan Lee, Seung-Yeop |
| author_facet | Duits, Maurice Hayford, Nathan Lee, Seung-Yeop |
| citation_txt | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function. Maurice Duits, Nathan Hayford and Seung-Yeop Lee. SIGMA 21 (2025), 079, 90 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-15T01:01:11Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214089 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T01:01:11Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Duits, Maurice Hayford, Nathan Lee, Seung-Yeop 2026-02-19T11:09:22Z 2025 The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function. Maurice Duits, Nathan Hayford and Seung-Yeop Lee. SIGMA 21 (2025), 079, 90 pages 1815-0659 2020 Mathematics Subject Classification: 30E15; 30E10; 30E25; 41A60; 05C30; 05C10 arXiv:2405.03259 https://nasplib.isofts.kiev.ua/handle/123456789/214089 https://doi.org/10.3842/SIGMA.2025.079 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. MD was supported by the Swedish Research Council (VR), grant no. 2021-06015, and the European Research Council (ERC), Grant Agreement No. 101002013. NH was supported by the European Research Council (ERC), Grant Agreement No. 101002013. Part of the work was completed while NH was at the University of South Florida. We would like to thank an anonymous referee, who pointed out some results in the literature that rigorously derive the genus-zero free energy using combinatorial methods. We would also like to thank all of the referees, whose valuable comments helped improve the overall presentation of this manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function Article published earlier |
| spellingShingle | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function Duits, Maurice Hayford, Nathan Lee, Seung-Yeop |
| title | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function |
| title_full | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function |
| title_fullStr | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function |
| title_full_unstemmed | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function |
| title_short | The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function |
| title_sort | ising model coupled to 2d gravity: genus zero partition function |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214089 |
| work_keys_str_mv | AT duitsmaurice theisingmodelcoupledto2dgravitygenuszeropartitionfunction AT hayfordnathan theisingmodelcoupledto2dgravitygenuszeropartitionfunction AT leeseungyeop theisingmodelcoupledto2dgravitygenuszeropartitionfunction AT duitsmaurice isingmodelcoupledto2dgravitygenuszeropartitionfunction AT hayfordnathan isingmodelcoupledto2dgravitygenuszeropartitionfunction AT leeseungyeop isingmodelcoupledto2dgravitygenuszeropartitionfunction |