Related papers: Non-analyticity in the large N renormalization gro…
Nonanalyticities of thermodynamic functions are studied by adopting an approach based on stationary points of the potential energy. For finite systems, each stationary point is found to cause a nonanalyticity in the microcanonical entropy,…
We introduce a method, based on an exact calculation of the effective action at large N, to bridge the gap between mean field theory and renormalization in complex systems. We apply it to a d-dimensional manifold in a random potential for…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion,…
We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d…
We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue density vanishes as an arbitrary real power at the origin, thus…
In this paper we study the analyticity of the group action of the automorphism group $G$ of a formal module $\bar{F}$ of height 2 (defined over $\overline{\mathbb{F}}_q$) on the Lubin-Tate deformation space $X$ of $\bar{F}$. It is shown…
Recently, the connections between gradient flow and renormalization group have been explored analytically and numerically. Gradient flow (when modified by a field rescaling) can be characterized as a continuous blocking transformation. In…
We examine the renormalization group flow in the vicinity of the free-field fixed point for effective field theories in the presence of a constant, nondynamical vector potential background. The interaction with this vector potential…
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…
A so-called Renormalization Group (RG) analysis is performed in order to shed some light on why the density of prime numbers in $\Bbb N^*$ decreases like the single power of the inverse neperian logarithm.
We derive an exact renormalization group recursion relation for the Loschmidt amplitude of the quantum $Q$-state clock model and the quantum $Q$-state Potts model in one dimension. The renormalization group flow is discussed in detail. The…
Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…
This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting…
We make an attempt to map a simple economically motivated model for the price evolution [J. Phys. A: Gen. Math 33, 3637 (2000)] to the phenomenological renormalization group scaling of stock markets. This mapping gives insight into the…
The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact…
In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum…
We define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric, $\g \to \lambda^2 \g$. We consider explicitly the case of a scalar field,…
Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…