Related papers: Universality, marginal operators, and limit cycles
Renormalization group limit cycles may be a commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience to date with classical models of critical points, where fixed points are far more common. We discuss the…
A simple example is used to show that renormalization group limit cycles of effective quantum theories can be studied in a new way. The method is based on the similarity renormalization group procedure for Hamiltonians. The example contains…
Schr\"odinger equation with potential $-g/r^2$ exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at $r=0$. Instead, we use the renormalization group…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
We study a simple class of unitary renormalization group transformations governed by a parameter f in the range [0,1]. For f=0, the transformation is one introduced by Wegner in condensed matter physics, and for f=1 it is a simpler…
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various…
Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents $\eta$ and $\delta$, as well as ratios of…
We consider the smallest eigenvalues of perturbed Hermitian operators with zero modes, either topological or system specific. To leading order for small generic perturbation we show that the corresponding eigenvalues broaden to a Gaussian…
A matrix model of an asymptotically free theory with a bound state is solved using a perturbative similarity renormalization group for hamiltonians. An effective hamiltonian with a small width, calculated including the first three terms in…
We introduce a universal criterion for criticality in mean-field rotor Hamiltonians based on the geometric structure of the constant-energy shell. Rather than characterizing the onset of a phase transition through the conventional…
We study how the finite-sized n-component model A with periodic boundary conditions relaxes near its bulk critical point from an initial nonequilibrium state with short-range correlations. Particular attention is paid to the universal…
A model Hamiltonian that exhibits asymptotic freedom and a bound state, is used to show on example that similarity renormalization group procedure can be tuned to improve convergence of perturbative derivation of effective Hamiltonians,…
In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We explain why it is important to require them to be eigenoperators and why generically they appear only as a consequence of…
The canonical quantum Hamiltonian eigenvalue problem for an anharmonic oscillator with a Lagrangian L = \dot{\phi}^2/2 - m^2 \phi^2/2 - g m^3 \phi^4 is numerically solved in two ways. One of the ways uses a plain cutoff on the number of…
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 derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
As in two and four dimensions, supersymmetric conformal field theories in three dimensions can have exactly marginal operators. These are illustrated in a number of examples with N=4 and N=2 supersymmetry. The N=2 theory of three chiral…
Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
The continuous block spin (Wilson) renormalization group equation governing the scale dependence of the action is constructed for theories containing scalars and fermions. A locally approximated form of this equation detailing the structure…