Title: Revisiting (logarithmic) scaling relations using renormalization group,
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.