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arXiv:1202.3481 · Brazilian Journal of Physics

Sine-Gordon Model: Renormalization Group Solution and Applications

Mariana Malard

Published Mar 21, 2013• 16 citations
arXivHTMLPDF
DOI
10.1007/s13538-013-0123-4

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The scheme dependence of the renormalization group (RG) flow has been investigated in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoretic models discussing the applicability of various functional RG methods in detail. It was shown that scheme-independent determination of such physical parameters is possible as the critical frequency (temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition takes place in the sine-Gordon and the layered sine-Gordon models, and the critical ratio characterizing the Ising-type phase transition of the massive sine-Gordon model. For the latter case, the Maxwell construction represents a strong constraint on the RG flow, which results in a scheme-independent infrared value for the critical ratio. For the massive sine-Gordon model also the shrinking of the domain of the phase with spontaneously broken periodicity is shown to take place due to the quantum fluctuations.
The quantum sine-Gordon model in two spatial dimensions is studied using the method of Wilson's renormalization group with the aid the Feynman path integral. The Kosterlitz-Thouless transition temperature is calculated and shown to be lower than that of the corresponding classical sine-Gordon model. A classical film system is shown to correspond to the quantum sine-Gordon model and its transition temperature is shown to increase with increasing thickness. Applicability of our treatment is examined.