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 ${\varphi }^n$-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 $ξ\sim L (\log L)^{\hat{\coppa}}$] and, finally, we have found a new derivation of the scaling law associated with it.

10 pages

References in corpus (8)

• Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
• Finite-size Scaling and Universality above the Upper Critical Dimensionality
• Scaling Relations for Logarithmic Corrections
• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions
• Numerical revision of the universal amplitude ratios for the two-dimensional 4-state Potts model
• The Site-Diluted Ising Model in Four Dimension

Cited by in corpus (5)

• Universal Finite-Size Scaling for Percolation Theory in High Dimensions
• Spin-glass dynamics: experiment, theory and simulation
• Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field
• Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna
• On a previously unpublished work with Ralph Kenna