相关论文: Critical Exponents near a Random Fractal Boundary
We consider quadrangulations with a boundary and derive explicit expressions for the generating functions of these maps with either a marked vertex at a prescribed distance from the boundary, or two boundary vertices at a prescribed mutual…
We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the…
The critical dynamics of conformal field theories on random surfaces is investigated beyond the previously studied dynamics of the overall area and the genus. It is found that the evolution of the order parameter in physical time performs a…
We study the boundary effects in invasion percolation with and without trapping. We find that the presence of boundaries introduces a new set of surface critical exponents, as in the case of standard percolation. Numerical simulations show…
We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not…
In a semi-infinite geometry, a 1D, M-component model of biological evolution realizes microscopically an inhomogeneous branching process for $M \to \infty$. This implies in particular a size distribution exponent $\tau'=7/4$ for avalanches…
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
Using field theoretic renormalization group methods we study the critical behavior of a driven diffusive system near a boundary perpendicular to the driving force. The boundary acts as a particle reservoir which is necessary to maintain the…
Correlation functions are sensitive to the presence of a boundary. Surface modulations give rise to modified near surface correlations, which can be measured by scattering probes. To determine these correlations, we develop a perturbative…
The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at…
This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
Generalized multifractality characterizes system size dependence of pure scaling local observables at Anderson transitions in all ten symmetry classes of disordered systems. Recently, the concept of generalized multifractality has been…
In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface. The modified near…
We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…
The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented…
The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality:…
Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close…
Two-dimensional directed site percolation is studied in systems directed along the x-axis and limited by a free surface at y=\pm Cx^k. Scaling considerations show that the surface is a relevant perturbation to the local critical behaviour…