Related papers: MCRG Flow for the nonlinear Sigma Model
We study the non-perturbative renormalization group flow of the nonlinear O(N) sigma model in two and three spacetime dimensions using a scheme that combines an effective local Hybrid Monte Carlo update routine, blockspin transformations…
We study the renormalization group flow of the O(N) non-linear sigma model in arbitrary dimensions. The effective action of the model is truncated to fourth order in the derivative expansion and the flow is obtained by combining the…
We describe a method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. It can be used, e.g., for lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and…
The renormalization group flow of an integrable two dimensional quantum field theory which contains unstable particles is investigated. The analysis is carried out for the Virasoro central charge and the conformal dimensions as a function…
We present a way to visualize and quantify renormalization group flows in a space of observables computed using Monte Carlo simulations. We apply the method to classical three-dimensional clock models, i.e., the planar (XY) spin model…
Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely…
We present a nonperturbative renormalization group solution of the Gell-Mann--Levy $\sigma$-model which was originally proposed as a phenomenological description of the dynamics of nucleons and mesons. In our version of the model the…
We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential…
Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and…
We describe a new method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. The method can be used for a general class of models, e.g., lattice spin or gauge models. The basic idea is to simulate…
The renormalized trajectory (RT) is determined from two different Monte Carlo renormalization group techniques with $\delta$-function block spin transformation in the multi-dimensional coupling parameter space of the two-dimensional…
We report current progress on the synthesis of methods to alleviate two major difficulties in implementing a Monte Carlo Renormalization Group (MCRG) for quantum systems. In particular, we have utilized the loop-algorithm to reduce critical…
We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S = \int d^dx \sqrt{g} f(R)$. Based on this equation we show that certain…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…
Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group…
We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field…
The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this…
The spin 1/2 XXZ chain in a random magnetic field pointing in the Z direction is numerically studied using the Density Matrix Renormalization Group (DMRG) method. The phase diagram as a function of the anisotropy of the XXZ Hamiltonian and…
The renormalized trajectory in the multi-dimensional coupling parameter space of the two-dimensional O(3) non-linear sigma model is determined numerically under \linebreak $\delta$-function block spin transformations using two different…
We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional Renormalization Group as a novel technique to compute the corresponding interacting fixed point of the…