Revisiting (logarithmic) scaling relations using renormalization group - Ruiz-Lorenzo, J.J. (Condensed Matter Physics, 2017)
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 φ 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 ϙˆ exponent [defined by ξ ∼ L(logL) ϙˆ ] and, finally, we have found a new derivation of the scaling law associated with it.