Ordered phase of the O(N) model within the nonperturbative renormalization group
Related Experiment Video
Updated: Mar 12, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Marcela Peláez1, Nicolás Wschebor1
1Instituto de Física, Facultad de Ingeniería, Universidad de la República, J.H.y Reissig 565, 11000 Montevideo, Uruguay.
Abstract:
We analyze nonperturbative renormalization group flow equations for the ordered phase of Z_{2} and O(N) invariant scalar models. This is done within the well-known derivative expansion scheme. For its leading order [local potential approximation (LPA)], we show that not every regulator yields a smooth flow with a convex free energy and discuss for which regulators the flow becomes singular. Then we generalize the known exact solutions of smooth flows in the "internal" region of the potential and exploit these solutions to implement an improved numerical algorithm, which is much more stable than previous ones for N>1. After that, we study the flow equations at second order of the derivative expansion and analyze how and when the LPA results change. We also discuss the evolution of the field renormalization factors.
Related Concept Videos
The Phase Rule
Phase Diagram
Phase Diagram
Phase Transitions
Phase Transitions
Phase Diagrams

