Indications of isotropic Lifshitz points in four dimensions

Abstract

The presence of isotropic Lifshitz points for a U(1) symmetric scalar theory is investigated with the help of the Functional Renormalization Group at the conjectured lower critical dimension d=4. To this aim, a suitable truncation in the expansion of the effective action in powers of the field is considered and, consequently, the Renormalization Group flow is reduced to a set of ordinary differential equations for the parameters that define the effective action. Within this approximation, indications of a line of Lifshitz points are found, that present evident similarities with the properties shown by the line of fixed points observed in the two dimensional Berezinsky-Kosterlitz-Thouless phase. In particular, this line of Lifshitz points exhibits the vanishing of the expectation value of the field, together with a finite stiffness and, for specific combinations of the parameters that define the effective action, also the algebraic decay at large distance of the order parameter correlations.

10 pages, 6 figures

References in corpus (10)

• Quantum Gravity at a Lifshitz Point
• Exact evolution equation for the effective potential
• Inhomogeneous chiral condensates
• Ising exponents from the functional renormalisation group
• Asymptotic freedom in Horava-Lifshitz gravity
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• Isotropic Lifshitz critical behavior from the functional renormalization group
• Uncovering novel phase structures in ${\square }^k$ scalar theories with the renormalization group
• Compatibility of 1/n and epsilon expansions for critical exponents at m-axial Lifshitz points

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• Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points
• Isotropic Lifshitz Scaling in four dimensions
• Ultraviolet properties of Lifshitz-type scalar field theories
• Lorentz symmetry violating Lifshitz-type field theories
• On the regularization of Lifshitz-type field theories
• RG studies of scalar-field models of long-range interactions
• Higher-derivative four-dimensional sine-Gordon model