Renormalisation group determination of scalar mass bounds in a simple Yukawa-model

The scalar mass is determined in the simplest cut-off regularized Yukawa-model in the whole range of stability of the scalar potential. Two versions of the Functional Renormalisation Group (FRG) equations are solved in the Local Potential Approximation (LPA), where also the possible existence of a composite fermionic background is taken into account. The close agreement of the results with previous studies taking into account exclusively the effect of the scalar condensate, supports a rather small systematic truncation error of FRG due to the omission of higher dimensional operators.

A COMPARED ANALYSIS OF THE SUSCEPTIBILITY IN THE O(N) THEORY

The longitudinal susceptibility χL of the O(N) theory in the broken phase is analyzed by means of three different approaches, namely the leading contribution of the 1/N expansion, the Functional Renormalization Group flow in the Local Potential approximation and the improved effective potential via the Callan–Symanzik equations, properly extended to d = 4 dimensions through the expansion in powers of ϵ = 4-d. The findings of the three approaches are compared and their agreement in the large N limit is shown. The numerical analysis of the Functional Renormalization Group flow equations at small N supports the vanishing of [Formula: see text] in d = 3 and d = 3.5 but is not conclusive in d = 4, where we have to resort to the Callan–Smanzik approach. At finite N as well as in the limit N→∞, we find that [Formula: see text] vanishes with J as Jϵ/2 for ϵ> 0 and as ( ln (J))-1 in d = 4.