2025/07/30 by Hayford, Nathan
#Complex Variables (math.CV) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2507.22646
We analyze the asymptotic properties a special solution of the (3,4) string equation, which appears in the study of the multicritical quartic 2-matrix model. In particular, we show that in a certain parameter regime, the corresponding τ-function has an asymptotic expansion which is `topological' in nature. Consequently, we show that this solution to the string equation with a specific set of Stokes data exists, at least asymptotically. We also demonstrate that, along specific curves in the parameter space, this τ-function degenerates to the τ-function for a tritronquée solution of Painlevé I (which appears in the critical quartic 1-matrix model), indicating that there is a `renormalization group flow' between these critical points. This confirms a conjecture from [1]. [1] The Ising model, the Yang-Lee edge singularity, and 2D quantum gravity, C. Crnković, P. Ginsparg, G. Moore. Phys. Lett. B 237 2 (1990)