The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Authors: Duits, Maurice, Hayford, Nathan, Lee, Seung-Yeop
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/214089
• 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

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...