Related papers: Quantum renormalization group approach to geometri…
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…
We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps, we find with exact…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples.…
A recently proposed curvature renormalization group scheme for topological phase transitions defines a generic `curvature function' as a function of the parameters of the theory and shows that topological phase transitions are signalled by…
Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for…
The quantum critical behavior and the Griffiths-McCoy singularities of random quantum Ising ferromagnets are studied by applying a numerical implementation of the Ma-Dasgupta-Hu renormalization group scheme. We check the procedure for the…
In the context of real-space renormalization group methods, we propose a novel scheme for quantum systems defined on a D-dimensional lattice. It is based on a coarse-graining transformation that attempts to reduce the amount of entanglement…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
We have analysed here the role of the geometric phase in dynamical mechanism of quantum phase transition in the transverse Ising model. We have investigated the system when it is driven at a fixed rate characterized by a quench time…
Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…
We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a…
We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of…
A renormalization-group scheme is developed for the 3-dimensional O($2N$)-symmetric Ginzburg-Landau-Wilson model, which is consistent with the use of a 1/N expansion as a systematic method of approximation. It is motivated by an application…
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…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution…