Condensed Matter Physics, 2017, vol. 20, No. 1, 13601
DOI:10.5488/CMP.20.13601           arXiv:1702.05072

Title: Revisiting (logarithmic) scaling relations using renormalization group
  J.J. Ruiz-Lorenzo (Departamento de Física, Universidad de Extremadura, 06071 Badajoz, Spain; Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz, Spain; Instituto de Biocomputación y Física de los Sistemas Complejos (BIFI), Zaragoza, Spain)

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 φn-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 exponent [defined by ξ∼L(log L)] and, finally, we have found a new derivation of the scaling law associated with it.

Key words: renormalization group, scaling, logarithms, mean field
PACS: 64.60-j,05.50+q,05.70.Jk,75.10.Hk

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