Related papers: Renormalization Group Study of Sandpile on the Tri…
The general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be…
We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration and radius of the avalanches will be…
Following the Renormalization Group scheme recently developed by Pietronero {\it et al}, we introduce a simplifying strategy for the renormalization of the relaxation dynamics of sandpile models. In our scheme, five sub-cells at a generic…
Kinetic equations, which explicitly take into account the branching nature of sandpile avalanches, are derived. The dynamics of the sandpile model is described by the generating functions of a branching process. Having used the results…
We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it…
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…
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 consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical…
One important step in the renormalization group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we propose a computer…
We study the problem of a random walk on a lattice in which bonds connecting nearest neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to…
For certain hierarchical structures, one can study the percolation problem using the renormalization-group method in a very precise way. We show that the idea can be also applied to two-dimensional planar lattices by regarding them as…
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 the renormalization group evolution up to the fixed point of the lattice topological susceptibility in the 2-d O(3) non-linear sigma-model. We start with a discretization of the continuum topological charge by a local charge…
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…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
The renormalization group has played an important role in the physics of the second half of the twentieth century both as a conceptual and a calculational tool. In particular it provided the key ideas for the construction of a qualitative…
The paper develops one-parametric family of the sand-piles dealing with the grains' local losses on the fixed amount. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean height of the…
The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent…
We analyze in some detail a recently proposed transfer matrix mean field approximation which yields the exact critical point for several two dimensional nearest neighbor Ising models. For the square lattice model we show explicitly that…
The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same…