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Revisiting (logarithmic) scaling relations using renormalization group

Revisiting (logarithmic) scaling relations using renormalization group

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) an...

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Bibliographic Details
Main Author: Ruiz-Lorenzo, J.J.
Format: Article
Language:English
Published: Інститут фізики конденсованих систем НАН України 2017
Series:Condensed Matter Physics
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/156547
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Summary: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.

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