相关论文: Asymptotic safety and field parametrization depend…

Two common approaches in low-rank optimization problems are either working directly with a rank constraint on the matrix variable, or optimizing over a low-rank factorization so that the rank constraint is implicitly ensured. In this paper,…

The multicritical generalizations of the Lee-Yang universality class arise as renormalization-group fixed points of scalar field theories with complex $i\varphi^{2n+1}$ interaction, $n\in\mathbb{N}$, just below their upper critical…

In conventional relativistic quantum field theory, the discrete operators $\textbf{C}$, $\textbf{P}$, and $\textbf{T}$ are matrix operators with no renormalization scale dependence. However, in a Lorentz-violating theory with a fermion…

Motivated by the conjecture that the cosmological constant problem could be solved by strong quantum effects in the infrared we use the exact flow equation of Quantum Einstein Gravity to determine the renormalization group behavior of a…

The asymptotic safety program builds on a high-energy completion of gravity based on the Reuter fixed point, a non-trivial fixed point of the gravitational renormalization group flow. At this fixed point the canonical mass-dimension of…

These lecture notes provide a pedagogical introduction to a specific continuum implementation of the Wilsonian renormalization group, the effective average action. Its general properties and, in particular, its functional renormalization…

We introduce a Renormalization scheme for the one and two dimensional Forest-Fire models in order to characterize the nature of the critical state and its scale invariant dynamics. We show the existence of a relevant scaling field…

We investigate multicritical phenomena in O(N)+O(M)-models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To…

A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…

Recent results based on renormalization group approaches to Quantum Gravity suggest that the Newton's and cosmological constants should be treated as dynamical variables whose evolution depend on the characteristic energy scale of the…

It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$…

We outline a separable matrix ansatz for the potentials in effective field theories of nonrelativistic two-body systems with short-range interactions. We use this ansatz to construct new fixed points of the renormalisation-group equation…

This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…

We study the application of the grouped fixed effects approach to binary choice models for panel data in presence of severe complete separation. Through data loss, complete separation may lead to biased estimates of Average Partial Effects…

The field theoretic renormalization group is applied to a simple model of random walk on a rough fluctuating surface. We consider the Fokker--Planck equation for a particle in a uniform gravitational field. The surface is modelled by the…

Nontrivial fixed points of the hierarchical renormalization group are computed by numerically solving a system of quadratic equations for the coupling constants. This approach avoids a fine tuning of relevant parameters. We study the…

We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…

Building a consistent Quantum Theory of Gravity is one of the most challenging aspects of modern theoretical physics. In the past couple of years, new attempts have been made along the path of ``asymptotic safety'' through the use of Exact…

Within the conformally reduced gravity model, where the metric is parametrised by a function $f(\phi)$ of the conformal factor $\phi$, we keep dependence on both the background and fluctuation fields, to local potential approximation and…

A perturbative quantum theory of the two Killing vector reduction of Einstein gravity is constructed. Although the reduced theory inherits from the full one the lack of standard perturbative renormalizability, we show that strict cutoff…