Related papers: Robustness of the O($N$) universality class
We derive the equation of the critical curve and calculate the renormalized masses of the $SO(N)$-symmetric $\lambda\phi^{4}$ model in the presence of a homogeneous external source. We do this using the Gaussian-Perturbative approximation…
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…
We consider the critical behaviour of long-range $O(n)$ models ($n \ge 0$) on ${\mathbb Z}^d$, with interaction that decays with distance $r$ as $r^{-(d+\alpha)}$, for $\alpha \in (0,2)$. For $n \ge 1$, we study the $n$-component…
The solution of the O$(N) \phi^4$ scalar field theory in the broken phase is given in the framework of light cone quantization and a 1/N expansion. It involves the successive building of operator solutions to the equation of motion and…
The renormalized zero-momentum four-point coupling $g_r$ of $O(N)$-invariant scalar field theories in $d$ dimensions is studied by applying the $1/N$ expansion and strong coupling analysis. The $O(1/N)$ correction to the $\beta$-function…
Four-fermi models in dimensionality $2<d<4$ exhibit an ultra-violet stable renormalization group fixed point at a strong value of the coupling constant where chiral symmetry is spontaneously broken. The resulting field theory describes…
We study a class of Lorentz violating quantum field theories that contain higher space derivatives, but no higher time derivatives, and become renormalizable in the large N expansion. The fixed points of their renormalization-group flows…
We solve analytically the renormalization-group equation for the potential of the O(N)-symmetric scalar theory in the large-N limit and in dimensions 2<d<4, in order to look for nonperturbative fixed points that were found numerically in a…
In this work, we use a specific parameterization of the hypergeometric approximants ( the one by Mera et.al in Phys. Rev. Let. 115, 143001 (2015)) to approximate the seven-loop critical exponent $\nu$ for the $O(2)$-symmetric $\phi^4$…
The renormalized zero-momentum four-point coupling $g_r$ of O(N)-invariant scalar field theories in $d$ dimensions is studied by applying the 1/N expansion and strong coupling analysis. The O(1/N) correction to the $\beta$-function and to…
We compute critical exponents of O(N) models in fractal dimensions between two and four, and for continuos values of the number of field components N, in this way completing the RG classification of universality classes for these models. In…
The scaling behaviour of euclidean quantum gravity at an asymptotically safe critical point is studied by means of the exact renormalisation group. Gauge independence is ensured via a specific parameterisation of metric fluctuations…
We introduce the Callan-Symanzik method in the description of anisotropic as well as isotropic Lifshitz critical behaviors. Renormalized perturbation theories are defined by normalization conditions with nonvanishing masses and at zero…
We consider $\phi^4$ theory with $\phi(x)\in\mathbb{R}$ in two Euclidean dimensions. We determine for a variety of self-couplings $\hat{\lambda}$ the (negative) critical bare mass $\hat{\mu}_{0\mathrm{c}}^2(\hat{\lambda})$ where the…
We formulate the simplest minimal subtraction version for massive $\lambda \phi^4$ scalar fields with $O(N)$ symmetry for generic anisotropic Lifshitz space-times. An appropriate partial$-p$ operation is applied in the bare two-point vertex…
New field theoretic renormalization group methods are developed to describe in a unified fashion the critical exponents of an m-fold Lifshitz point at the two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close to 8)…
We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not…
The critical behavior of a non-local scalar field theory is studied. This theory has a non-local quartic interaction term which involves a real power -\beta of the Laplacian. The parameter \beta can be tuned so as to make that interaction…
We review recent activity in the construction of the renormalization group functions for O(N) scalar and gauge theories in six and higher dimensions. The theories lie in their respective universality classes at the Wilson-Fisher fixed…
Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\phi^*\phi)^2$ theory may be computed semi-classically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$ and this was…