Optimization of the derivative expansion in the nonperturbative renormalization group

TL;DR

This paper investigates optimizing nonperturbative renormalization group equations using the Principle of Minimal Sensitivity, improving critical exponent accuracy in the 3D Ising model through derivative expansion optimization.

Contribution

It demonstrates unambiguous implementation of the Principle of Minimal Sensitivity at order ∂², optimizing cut-off functions and analyzing convergence in the derivative expansion.

Findings

Optimized cut-off functions improve critical exponent estimates.

The convergence of the field expansion is analyzed and optimized.

Optimization of the field expansion differs from that of critical exponents.

Abstract

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be unambiguously implemented at order $\partial^2$ of the derivative expansion. This approach allows us to select optimized cut-off functions and to improve the accuracy of the critical exponents $\nu$ and $\eta$. The convergence of the field expansion is also analyzed. We show in particular that its optimization does not coincide with optimization of the accuracy of the critical exponents.