Year: 2026
Type: preprint
Abstract: A novel physics-informed neural networks (PINNs) based approach for solving functional renormalization group flow equations is presented. We investigate the finite temperature phase transition in $O(N)$ models without relying on the large-$N$ approximation, which was used in earlier attempts with similar methods. We argue that these previous solutions cannot easily be generalized for more complex symmetries, and hence our approach can provide new insight. Our technique relies on a series of ansätze that combines the small- and large-field approximation schemes with a neural network, leading to a highly accurate approximation over the entire field range. We compare the PINNs approach with traditional grid-based Runge-Kutta results and show that the network can successfully learn the temperature, field, and scale dependencies of the effective potential in the local potential approximation.
Source: arXiv (Cornell University)
Authors: Gurzó, J., Fejős, G.
Institutions: Eötvös Loránd University, Brookhaven National Laboratory
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221536053