Critical equation of state from the average action

TL;DR

This paper derives the critical equation of state for $O(N)$ models using an exact flow equation approach, providing a numerical solution for the scaling behavior near criticality.

Contribution

It introduces a novel method based on an exact flow equation for coarse grained free energy to compute the critical equation of state.

Findings

Derived the scaling form of the critical equation of state for $O(N)$ models

Numerically solved the flow equation with a suitable truncation

Provided insights into the critical behavior of $O(N)$-symmetric systems

Abstract

The scaling form of the critical equation of state is computed for $O(N)$-symmetric models. We employ a method based on an exact flow equation for a coarse grained free energy. A suitable truncation is solved numerically.