Related papers: Renormalization group flows in a Lifshitz-like fou…
Without Lorentz symmetry, generic fixed points of the renormalization group (RG) are labelled by their dynamical (or `Lifshitz') exponent $z$. Hence, a rich variety of possible RG flows arises. The first example is already given by the…
We study the one-loop renormalization of high-energy Lorentz violating four fermion models. We derive general formulas and then consider a number of specific models. We study the conditions for asymptotic freedom and give a practical method…
This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group…
A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses…
A new renormalization group treatment is proposed for the critical exponents of an m-fold Lifshitz point. The anisotropic cases (m not equal 8) are described by two independent fixed points associated to two independent momentum flow along…
We construct the general renormalizable actions for the scalar field and the gauge field at a Lifshitz point characterized by the dynamical critical exponent $z$. The Lorentz invariance is broken down in the UV region, but is recovered in…
We present the lattice simulation of the renormalization group flow in the $3$-dimensional $O(N)$ linear sigma model. This model possesses a nontrivial infrared fixed point, called Wilson--Fisher fixed point. Arguing that the parameter…
We consider an interacting Lifshitz field with z=3 in a curved spacetime. We analyze the renormalizability of the theory for interactions of the form lambda phi^n, with arbitrary even n. We compute the running of the coupling constants both…
The stability of nonrelativistic fermionic systems to interactions is studied within the Renormalization Group framework. A brief introduction to $\phi^4$ theory in four dimensions and the path integral formulation for fermions is given.…
We study the one-loop renormalization and evolution of the couplings in scalar field theories of the Lifshitz type, i.e. with different scaling in space and time. These theories are unitary and renormalizable, thanks to higher spatial…
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…
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)…
The Lifshitz critical behavior for a single component field theory is studied for the specific isotropic case in the framework of the Functional Renormalization Group. Lifshitz fixed point solutions of the flow equation, derived by using a…
We study renormalization group flows in strongly interacting field theories with fermions that correspond to transitions between a theory without Lorentz invariance at high energies down to a theory with approximate Lorentz symmetry in the…
Motivated by recent attempts to find nontrivial infrared fixed points in 4-dimensional lattice gauge theories, we discuss the extension of the renormalization group (RG) transformations to complex coupling spaces for O(N) models on LxL…
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 the Nambu--Jona-Lasinio model at finite temperature and finite density by using the functional renormalization group. The RG flows of the four-fermi coupling constant in the NJL model are investigated. We obtain the chiral phase…
A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form $\phi\,\Box^k\phi$. We use the non-perturbative RG to study examples of flows between such fixed points. We show that the anomalous…
The purpose of this paper is to present our study on the restoration of the Lorentz symmetry for a Lifshitz-type scalar theory in the infrared region by using nonperturbative methods. We apply the Wegner-Houghton equation, which is one of…
Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ by Chatterjee \emph{et al.} [Nature Physics \textbf{6}, 99 (2010)], we perform a field-theoretical…