Derivative expansion and renormalisation group flows

TL;DR

This paper investigates how the choice of infrared regularisation affects the convergence of derivative expansion in flow equations, demonstrating that optimized regulators enhance the accuracy of critical exponent predictions in scalar field theories.

Contribution

It explains why optimized regulators improve physical predictions and applies this insight to compute critical exponents in 3d O(N) models, showing up to 10% improvement over sharp cut-off.

Findings

Optimized regulators lead to better physical predictions.

Critical exponents are computed for all N in 3d O(N) models.

Improvement of up to 10% over sharp cut-off results.

Abstract

We study the convergence of the derivative expansion for flow equations. The convergence strongly depends on the choice for the infrared regularisation. Based on the structure of the flow, we explain why optimised regulators lead to better physical predictions. This is applied to O(N)-symmetric real scalar field theories in 3d, where critical exponents are computed for all N. In comparison to the sharp cut-off regulator, an optimised flow improves the leading order result up to 10%. An analogous reasoning is employed for a proper time renormalisation group. We compare our results with those obtained by other methods.