# Revisiting (logarithmic) scaling relations using renormalization group

## TL;DR

This paper uses renormalization group techniques to compute logarithmic correction exponents in critical phenomena, verifying scaling relations and introducing a new method to determine specific correction exponents.

## Contribution

It provides explicit calculations of logarithmic correction exponents from RG equations and mean field theory, and introduces a novel method for computing the  correction exponent.

## Key findings

- Verified scaling relations among logarithmic correction exponents.
- Developed an explicit method to compute the  exponent.
- Derived a new scaling law for the  correction exponent.

## Abstract

We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper critical behavior (for short and long range $\phi^n$-theories) and below it. This allows us to check the scaling relations among these critical exponents obtained by analysing the complex singularities (Lee-Yang and Fisher zeroes) of these models. Moreover, we have obtained an explicit method to compute the $\hat{\coppa}$ exponent [defined by $\xi\sim L (\log L)^{\hat{\coppa}}$] and, finally, we have found a new derivation of the scaling law associated with it.