Related papers: Correlations near the vulcanization transition: A …
Percolation clusters are probably the simplest example for scale--invariant structures which either are governed by isotropic scaling--laws (``self--similarity'') or --- as in the case of directed percolation --- may display anisotropic…
We explore the applicability of the exact renormalization group to the study of tunnelling phenomena. We investigate quantum-mechanical systems whose energy eigenstates are affected significantly by tunnelling through a barrier in the…
A recently proposed renormalization group approach to dimensional crossover in quasi-one-dimensional quantum antiferromagnets is improved and then shown to give identical results, in some cases, to those obtained earlier.
We analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature. We prove weak Gibbsianity of the renormalized measure and convergence of the…
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…
We study percolation on the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)},\; \delta >-1$. Since the distance is an ultrametric, there…
We point out some similitudes between the statistics of high Reynolds number turbulence and critical phenomena. An analogy is developed for two-dimensional decaying flows, in particular by studying the scaling properties of the two-point…
We study a system of weakly interacting electrons described by the energy dispersion $\xi(\mathbf{k}) = k_x^2 - k_y^2 - \mu$ in two dimensions within a renormalization group approach. This energy dispersion exhibits a neck-narrowing…
We study the effective theory of the conformal factor near its infrared stable fixed point.The renormalization group equations for the effective coupling constants are found and their solutions near the critical point are obtained,…
The two-point correlation function in thin films is studied near the critical point of the corresponding bulk system. Based on fieldtheoretic renormalization group theory the dependences of this correlation function on the lateral momentum,…
The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal…
The functional renormalisation group for the Einstein-Hilbert action is investigated for the case of four infinite (or large) and one compact dimension. The motivation for this study is given by the suggestion that gravity in more than four…
Using Wilson-Polchinski renormalization group equations, we give a simple new proof of decoupling in a $\phi^4$-type scalar field theory involving two real scalar fields (one is heavy with mass $M$ and the other light). Then, to all orders…
The overlap of a $d+1$ dimensional directed polymer of length $t$ in a random medium is studied using a Renormalization Group approach. In $d>2$ it vanishes at $T_c$ for $t\rightarrow \infty$ as $t^{\Sigma}$ where…
In the past two decades or so, we have learned how to understand crackling noise in a wide variety of systems. We review here the basic ideas and methods we use to understand crackling noise - critical phenomena, universality, the…
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…
We study a generalization of two-dimensional site percolation by assigning an energy cost $\varepsilon$ to bonds between nearest-neighbor occupied sites. This leads to a competition between entropy-driven cluster growth and energetic…
We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…
We conducted Monte Carlo simulations to analyze the percolation transition of a non-symmetric loop model on a regular three-dimensional lattice. We calculated the critical exponents for the percolation transition of this model. The…
The q-model is a random walk model used to describe the flow of stress in a stationary granular medium. Here we derive the exact horizontal and vertical correlation functions for the q-model in two dimensions. We show that close to a…