# Testing logarithmic violations to scaling in strongly coupled QED

## TL;DR

This paper investigates the critical behavior of non-compact QED4 with multiple flavors, finding that the data supports a pure power law scaling with non-mean-field exponents, challenging logarithmic violation models.

## Contribution

It provides the first precise analysis of the critical couplings in QED4, demonstrating that logarithmic violations are inconsistent with numerical data and favoring a pure power law scaling.

## Key findings

- Logarithmic violation models are definitively excluded by data.
- Pure power law scaling with non-mean-field exponents is favored.
- The behavior with the number of flavors supports non-mean-field critical exponents.

## Abstract

Using very precise measurements of the critical couplings for the chiral transition of non compact $QED_4$ with up to 8 flavours, we analyse the behaviour of the order parameter at the critical point using the equation of state of a logarithmically improved scalar mean field theory, that of the Nambu-Jona Lasinio theory and a pure power law. The first case is definitively excluded by the numerical data. The stability of the fits for the last two cases, as well as the behaviour with the number of flavours of the exponent of the logarithmic violations to the scaling favour clearly a pure power law scaling with non mean field exponents.