Related papers: Wilson RG of Noncommutative $\Phi_{4}^4$
We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to perturbative construction of the $\phi^4$ theory where the parameters of the theory are…
The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a quantum phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an…
We derive a supersymmetric renormalization group (RG) equation for the scale-dependent superpotential of the supersymmetric O(N) model in three dimensions. For a supersymmetric optimized regulator function we solve the RG equation for the…
We continue the study of the bosonic $O(N)^3$ model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant $\phi^4$ composite operators, known as tetrahedron, pillow and double-trace. As…
We discuss how the ordinary renormalization group (RG) equations arise in the context of Wilson's exact renormalization group (ERG) as formulated by Polchinski. We consider the phi4 theory in four dimensional euclidean space as an example,…
We study a Hermitian matrix model with a quartic potential, modified by a curvature term $\mathrm{tr}(R\Phi^2)$, where $R$ is a fixed external matrix. Inspired by the truncated Heisenberg algebra formulation of the Grosse--Wulkenhaar model,…
We study the renormalization invariant trajectory of the $\phi^4$-perturbation of the free field fixed point in the hierarchical approximation. We parametrize it by a running $\phi^4$-coupling $g$ with linear step $\beta$-function. We…
The Wilsonian renormalization group (RG) method is applied to finite temperature systems for the study of non-perturbative methods in the field theory. We choose the O(N) linear sigma model as the first step. Under the local potential…
In this article we calculate several divergent amplitudes in phi^4-theory on non-commutative space-time in the framework of Interaction Point Time Ordered Perturbation Theory (IPTOPT), continuing work done in hep-th/0209253. On the ground…
We study the quantization of the noncommutative selfdual \phi^3 model in 4 dimensions, by mapping it to a Kontsevich model. The model is shown to be renormalizable, provided one additional counterterm is included compared to the…
We study the sector of large charge operators $\phi^n$ ($\phi$ being the complexified scalar field) in the $O(2)$ Wilson-Fisher fixed point in $4-\epsilon$ dimensions that emerges when the coupling takes the critical value $g\sim \epsilon$.…
We write new functional renormalization group equations for a scalar nonminimally coupled to gravity. Thanks to the choice of the parametrization and of the gauge fixing they are simpler than older equations and avoid some of the…
In a previous work, we established perturbative renormalizability to all orders of the massive $\phi^4_4$-theory on a half-space also called the semi-infinite massive $\phi^4_4$-theory. Five counter-terms which are functions depending on…
The line of phase transitions, separating the confinement and the Coulomb phases in the four-dimensional pure compact U(1) gauge theory with extended Wilson action, is reconsidered. We present new numerical evidence that a part of this…
The Euclidean $(\phi^{4})_{3,\epsilon$ model in $R^3$ corresponds to a perturbation by a $\phi^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $\epsilon$ in the range $0\le \epsilon \le…
We compute renormalization group fixed points and their spectrum in an ultralocal approximation. We study a case of two competing non-trivial fixed points for a three-dimensional real $N$-component field: the O(N)-invariant fixed point…
We consider the quartic analogue of the Kontsevich model, which is defined by a measure $\exp(-{N}\,\mathrm{Tr}(E\Phi^2+(\lambda/4)\Phi^4)) d\Phi$ on Hermitian ${N}\times{N}$-matrices, where $E$ is any positive matrix and $\lambda$ a…
We report on a comprehensive analysis of the renormalization of noncommutative \phi^4 scalar field theories on the Groenewold-Moyal (GM) plane. These scalar field theories are twisted Poincar\'e invariant. Our main results are that these…
A hybrid of the critical three dimensional Gross-Neveu and Thirring models deformed by explicit parity breaking operators is studied in the large N expansion and using the renormalization group. The regime of coupling constants where the…
We investigate matrix models in three dimensions where the global $\text{SU}(N)$ symmetry acts via the adjoint map. Analyzing their ground state which is homogeneous in space and can carry either a unique or multiple fixed charges, we show…