Revisiting (logarithmic) scaling relations using renormalization group

• Main Author: J.J. Ruiz-Lorenzo
• Format: Article
• Language: English
• Published: Institute for Condensed Matter Physics 2017-03-01
• Series: Condensed Matter Physics
• Subjects: renormalization group; scaling; logarithms; mean field
• Online Access: https://doi.org/10.5488/CMP.20.13601

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 coppa exponent and, finally, we have found a new derivation of the scaling law associated with it.