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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2025 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214089 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| Zusammenfassung: | 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.
|
|---|---|
| ISSN: | 1815-0659 |