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arXiv · hep-th/0110134

Renormalization Group Equations and the Lifshitz Point In Noncommutative Landau-Ginsburg Theory

Guang-Hong Chen·Yong-Shi Wu
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Abstract

A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative $Θ$-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents $ν_m$ and $β_k$, whose values are determined to be 1/4 and 1/2, respectively, at mean-field level.

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Guang-Hong Chen, Yong-Shi Wu. 2001-10-15. Renormalization Group Equations and the Lifshitz Point In Noncommutative Landau-Ginsburg Theory. https://doi.org/10.1016/s0550-3213(01)00587-9

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