The Ising Model Coupled to 2D Gravity: Bigger-order Painlevé Equations/The (3,4) String Equation
Authors: Nathan Hayford
Abstract: In continuation of the work [1], we analysis a higher-order Painlevé-type equation, arising as a string equation of the third order low cost of the KP hierarchy. This equation appears on the multi-critical degree of the 2-matrix model with quartic interactions, and describes the Ising half transition coupled to 2D gravity. We characterize this equation relating to the isomonodromic deformations of a selected rational connection on P1. We moreover set up the (nonautonomous) Hamiltonian development associated to this equation, and write an acceptable τ-differential for this system. This τ-differential could also be extended to the canonical coordinates of the associated Hamiltonian system, allowing us to verify Conjectures 1. and a pair of. of [2] in our case. We moreover present a fairly widespread formulation for the τ-differential of a specific class of resonant connections, which is significantly simpler than that of [3]. [1] M. Duits, N. Hayford, and S.-Y. Lee. “The Ising Model Coupled to 2D Gravity: Genus Zero Partition Carry out”. arXiv preprint, 2023. [2] A.R. Its and A. Prokhorov. “On some Hamiltonian properties of the isomonodromic tau capabilities”. Rev. Math. Phys. 30.7 (2018). [3] M. Bertola and M.Y. Mo. “Isomonodromic deformation of resonant rational connections”. Int. Math. Res. Pap. 11 (2005).
