Exact renormalization group equation for the Lifshitz critical point

Abstract

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the $O({\epsilon }^2)$ calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations $O(\epsilon )$ finally unstable.

Final version

References in corpus (3)

• Exact Renormalization Group Equations. An Introductory Review
• Critical behavior at m-axial Lifshitz points: field-theory analysis and $\epsilon$-expansion results
• Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points

Cited by in corpus (13)

• An Introduction to the Nonperturbative Renormalization Group
• Renormalization group flow of Hořava-Lifshitz gravity at low energies
• Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class
• Fluctuation-induced forces in strongly anisotropic critical systems
• The Wilson-Polchinski exact renormalization group equation
• Large-n expansion for m-axial Lifshitz points
• Isotropic Lifshitz point in the O(N) Theory
• Isotropic Lifshitz critical behavior from the functional renormalization group
• Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion
• Indications of isotropic Lifshitz points in four dimensions
• Restoration of Lorentz Symmetry for Lifshitz-Type Scalar Theory
• A study of the (m,d,N)=(1,3,2) Lifshitz point and of the three- dimensional XY universality class by high-temperature bivariate series for the XY models with anisotropic competing interactions
• A Feynman integral in Lifshitz-point and Lorentz-violating theories in $R^D\oplus R^m$