Related papers: Computing the renormalization group flow of two-di…
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…
Irreversibility theorems -- such as the $A$-theorem -- establish a hierarchy among fixed points of the renormalization group flow. The strongest thesis of this type of theorems would be that there exists a scalar function $A$ (generally…
The global structure of the renormalization-group flows of a model with isotropic and cubic interactions is studied using the massive field theory directly in three dimensions. The four-loop expansions of the $\bt$-functions are calculated…
The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the…
We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order…
We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then…
We investigate the phase transition of the four-dimensional single-component $\phi^4$ theory on the lattice using the tensor renormalization group method. We have examined the hopping parameter dependence of the bond energy and the vacuum…
The general prescription for constructing the continuum limit of a field theory is explained using Wilson's renormalization group. We then formulate the renormalization group in perturbation theory and apply it to the four dimensional phi4…
Based upon the intrinsic relation between the divergent lower point functions and the convergent higher point ones in the renormalizable quantum field theories, we propose a new method for regularization and renormalization in QFT. As an…
We propose a general procedure for extracting the running coupling constants of the underlying field theory of a given classical statistical model on a two-dimensional lattice, combining tensor network renormalization (TNR) and the…
We present a new real space renormalization-group map, on the space of probabilities, to study the renormalization of the SUSY \phi^4. In our approach we use the random walk representation on a lattice labeled by an ultrametric space. Our…
We implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group (RG) approach.…
We present a simple and consistent way to compute correlation functions in interacting theories with non-trivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional…
We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
We show irreversibility of the renormalization group flow in non-unitary but ${\cal PT}$-invariant quantum field theory in two space-time dimensions. In addition to unbroken $\mathcal{PT}$-symmetry and a positive energy spectrum, we assume…
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced…
We consider renormalization group flows between conformal field theories in five (six) dimensions with a string (M-theory) dual. By compactifying on a circle (torus) with appropriate boundary conditions, we obtain continuous families of…
Techniques for approximately contracting tensor networks are limited in how efficiently they can make use of parallel computing resources. In this work we demonstrate and characterize a Monte Carlo approach to the tensor network…
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…