Related papers: Continuous Constructive Fermionic Renormalization
In the limit of many fermion flavors it is demonstrated that the sextic Gross-Neveu theory in three dimensions displays a line of interacting UV fixed points, characterised by an exactly marginal sextic interaction. We determine the…
We consider the O(N)-symmetric phi4 theory in two and three dimensions and determine the nonperturbative mass renormalization needed to obtain the phi4 continuum theory. The required nonperturbative information is obtained by resumming…
We apply pseudo-spectral methods to construct global solutions of functional renormalisation group equations in field space to high accuracy. For this, we introduce a basis to resolve both finite as well as asymptotic regions of effective…
Gross-Neveu model in 2+1 dimensions exhibits a continuous transition from gapless Dirac semimetal to the gapped quantum anomalous Hall (QAH) insulator at a finite (attractive) coupling, at which the inversion and time-reversal symmetry…
The lattice Sommerfield model, describing a massive vector gauge field coupled to a light fermion in 2d, is an ideal candidate to verify perturbative conclusions. In contrast with continuum exact solutions, we prove that there is no…
This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The third paper in the series presents a perturbative…
Layers of two-dimensional materials arranged at a twist angle with respect to each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states.…
We introduce two versions of a renormalization group scheme for the equal load sharing fiber bundle model. The renormalization group is based on formulating the fiber bundle model in the language of damage mechanics. A central concept is…
The rules for the free fermionic string model construction are extended to include general non-abelian orbifold constructions that go beyond the real fermionic approach. This generalization is also applied to the asymmetric orbifold rules…
We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional scalar theories. It is based on 1/N-expansion and results in a logarithmically divergent perturbation theory in…
In these proceedings, we discuss why functional renormalization is an essential tool to treat strongly disordered systems. More specifically, we treat elastic manifolds in a disordered environment. These are governed by a disorder…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
We demonstrate the efficiency of the bond weighting method for the Grassmann tensor renormalization group (TRG). Benchmarking with the two-dimensional Gross-Neveu model with the Wilson fermion at finite density, we show that the bond…
Random noncommutative geometry can be seen as a Euclidean path-integral approach to the quantization of the theory defined by the Spectral Action in noncommutative geometry (NCG). With the aim of investigating phase transitions in random…
An imitation of 2d field theory is formulated by means of a model on the hierarchic tree (with branching number close to one) with the same potential and the free correlators identical to those of 2d ones. Such a model possesses some…
A review of the renormalization group approach to the proof of non perturbative ultraviolet stability in scalar field theories in dimension d=2,3.
We probe the U(N) Gross-Neveu model with a source-term $J\bar{\Psi}\Psi$. We find an expression for the renormalization scheme and scale invariant source $\hat{J}$, as a function of the generated mass gap. The expansion of this function is…
The Gross-Neveu model in 1+1 dimensions is generalized to the case of different scalar and pseudoscalar coupling constants. This enables us to interpolate smoothly between the standard massless Gross-Neveu models with either discrete or…
Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry $Z\_{5}$. New fixed points are found…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…