Related papers: A renormalisation group method. IV. Stability anal…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
We present a functional renormalization group analysis of superconductivity in the ground state of the attractive Hubbard model on a square lattice. Spontaneous symmetry breaking is treated in a purely fermionic setting via anomalous…
We apply the functional renormalization group to an Abelian Group Field Theory extended beyond the branched-polymer (melonic) sector by including interactions that are subdominant from a power-counting perspective but enhanced by derivative…
The persistent current in a lattice model of a one-dimensional interacting electron system is systematically studied using a complex version of the density matrix renormalization group algorithm and the functional renormalization group…
We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the…
Summation of the perturbation series for the Gell-Mann--Low function \beta(g) of \phi^4 theory leads to the asymptotics \beta(g)=\beta_\infty g^\alpha at g\to\infty, where \alpha\approx 1 for space dimensions d=2,3,4. The natural hypothesis…
The standard approach to renormalization relies, technically, on the asymptotic perturbation of Gaussian measures embodied in Feynman diagram theory. From a mathematical standpoint this is not good enough, because thereby solving the…
We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
We present an analytic theory unraveling the microscopic mechanism of instabilities within interacting $D$-dimensional Fermi liquid. Our model consists of a $D$-dimensional electron gas subject to an instantaneous electron-electron…
The Renormalization Group flow equations obtained by means of a proper time regulator are used to analyze the restoration of the discrete chiral symmetry at non-zero density and temperature in the Gross-Neveu model in d=2+1 dimensions. The…
We use field theoretic renormalization group methods to study the critical behavior of a recently proposed Langevin equation for driven lattice gases under infinitely fast drive. We perform an expansion around the upper critical dimension,…
We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of…
We propose a regularization-independent method for studying a renormalizable field theory nonperturbatively through its Dyson-Schwinger equations. Using QED_4 as an example, we show how the coupled equations determining the nonperturbative…
By reviewing the application of the renormalization group to different theoretical problems, we emphasize the role played by the general symmetry properties in identifying the relevant running variables describing the behavior of a given…
The critical behaviour of a non-local scalar field theory is studied. This theory has a non-local kinetic term which involves a real power 1-2\alpha of the Laplacian. The interaction term is the usual local \phi^{4} interaction. The lowest…
These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature $T_c$ of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have…
We use perturbation theory to construct perfect lattice actions for fermions and gauge fields by blocking directly from the continuum. When one uses a renormalization group transformation that preserves chiral symmetry the resulting lattice…
An effective formalism for white noise analysis, conceptually equivalent to Wilsonian renormalization theory, is introduced. Space-time gets represented by a boolean lattice of coarse regions, energy scales become space-time partitions by…
The massive Schwinger model is studied, using a density matrix renormalisation group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit…