Enhancement of field renormalization in scalar theories via functional renormalization group

Abstract

The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the field in the broken phase. In our numerical analysis, the infrared limit, corresponding to the vanishing of the running momentum scale in the equations, is approached to obtain the physical values of the parameters by extrapolation. In the N=4 theory a non-perturbatively large value of the physical renormalization of the longitudinal component of the field is observed. The dependence of the field renormalization on the UV cut-off and on the bare coupling is also investigated.

20 pages, 7 figures. To appear in Physical Review D

References in corpus (7)

• Exact evolution equation for the effective potential
• Ising exponents from the functional renormalisation group
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• The non-perturbative renormalization group in the ordered phase
• Convexity of the effective action from functional flows
• Renormalization-Group flow for the field strength in scalar self-interacting theories

Cited by in corpus (11)

• Solving functional flow equations with pseudo-spectral methods
• Self-consistent Spectral Functions in the $O(N)$ Model from the FRG
• Vanishing Beta Function curves from the Functional Renormalisation Group
• Isotropic Lifshitz point in the O(N) Theory
• Universal behavior of coupled order parameters below three dimensions
• The ordered phase of $O(N)$ model within the Non-Perturbative Renormalization Group
• Isotropic Lifshitz critical behavior from the functional renormalization group
• Critical scaling in the large-$N$ $O(N)$ model in higher dimensions and its possible connection to quantum gravity
• Inflationary Potentials from the Exact Renormalisation Group
• Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models
• A compared analysis of the susceptibility in the O(N) theory