Related papers: RG-Improved Three-Loop Effective Potential of the …
The motivation and the challenge in applying the renormalization group for systems with several scaling regimes is briefly outlined. The four dimensional $\phi^4$ model serves as an example where a nontrivial low energy scaling regime is…
Using the renormalisation group and a conjecture concerning the perturbation series for the effective potential, the leading logarithms in the effective potential are exactly summed for $O(N)$ scalar and Yukawa theories.
We present the perturbative renormalization group functions of $O(n)$-symmetric $\phi^4$ theory in $4-2\varepsilon$ dimensions to the sixth loop order in the minimal subtraction scheme. In addition, we estimate diagrams without…
I present the effective potential at three-loop order for a general renormalizable theory, using the \MSbar renormalization scheme and Landau gauge fixing. As applications and illustrative points of reference, the results are specialized to…
We perform a detailed analysis of renormalization at one-loop order in the $\lambda\phi^4$ theory with Robin boundary condition (characterized by a constant $c$) on a single plate at $z=0$. For arbitrary $c\geq0$ the renormalized theory is…
It has been previously shown that calculation of renormalization group (RG) functions of the scalar \phi^4 theory reduces to the analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG…
I compute the two-loop effective potential in the Landau gauge for a general renormalizable field theory in four dimensions. Results are presented for the \bar{MS} renormalization scheme based on dimensional regularization, and for the…
Multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the Gildener & Weinberg (GW) method…
In this paper the phase structure of the massive $\lambda \phi^4$ model at finite temperature ($T \neq 0$) is investigated by applying a resummation method inspired by the renormalization-group (RG) improvement to the one-loop effective…
The inhomogeneous renormalization group equation for the effective potential is rederived. It is shown that when the effective potential is normalized by the normalization condition on the generating functional, its renormalization group…
The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal…
The renormalization-group (RG) functions for the three-dimensional n-vector cubic model are calculated in the five-loop approximation. High-precision numerical estimates for the asymptotic critical exponents of the three-dimensional impure…
We consider the scalar sector of a general renormalizable theory and evaluate the effective potential through three loops analytically. We encounter three-loop vacuum bubble diagrams with up to two masses and six lines, which we solve using…
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…
A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the…
The Standard MS renormalization prescription is inadequate for dealing with multi-scale problems. To illustrate this we consider the computation of the effective potential in the Higgs-Yukawa model. It is argued that it is natural to employ…
When one uses the Coleman-Weinberg renormalization condition, the effective potential $V$ in the massless $\phi_4^4$ theory with O(N) symmetry is completely determined by the renormalization group functions. It has been shown how the…
We consider a generic class of effective quantum field theories with arbitrary gauge groups and scalar matter fields. In such theories, we derive the one-loop Renormalization Group Equations (RGEs) for the physical dimension-six operators.…
We compute template formulae of all four-loop $\beta$-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the $\overline{\text{MS}}$ scheme. Using these results, novel…
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced…