Isotropic Lifshitz critical behavior from the functional renormalization group

Abstract

The Lifshitz critical behavior for a single component field theory is studied for the specific isotropic case in the framework of the Functional Renormalization Group. Lifshitz fixed point solutions of the flow equation, derived by using a Proper Time regulator, are searched at lowest and higher order in the derivative expansion. Solutions are found when the number of spatial dimensions d is contained within the interval 5.5 < d < 8.

Published version.Minor corrections and references added

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• Uncovering novel phase structures in ${\square }^k$ scalar theories with the renormalization group
• Indications of isotropic Lifshitz points in four dimensions
• Critical fluctuations in an optical parametric oscillator: when light behaves like magnetism
• Isotropic Lifshitz Scaling in four dimensions
• Ultraviolet properties of Lifshitz-type scalar field theories
• A Feynman integral in Lifshitz-point and Lorentz-violating theories in $R^D\oplus R^m$
• Lorentz symmetry violating Lifshitz-type field theories
• RG studies of scalar-field models of long-range interactions
• On the regularization of Lifshitz-type field theories
• Higher-derivative four-dimensional sine-Gordon model