相关论文: Percolation properties of the classic Sierpinski c…
We present a key algorithmic improvement to the generalized combinatorial Feynman--Vdovichenko method for calculating the critical temperature of the Ising model on Sierpinski carpets $SC_k(a,b)$, originally introduced in arxiv:1505.02699.…
We consider critical oriented Bernoulli percolation on the square lattice $\mathbb{Z}^2$. We prove a Russo-Seymour-Welsh type result which allows us to derive several new results concerning the critical behavior: - We establish that the…
Slicks are thin viscous films that can be found at the air--water interface of water bodies such as lakes, rivers and oceans. These micro-layers are enriched in surfactants, organic matter, and microorganisms, and exhibit steep physical and…
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 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 establish the theory of critical transport in amorphous Chern insulators and show that it lies beyond the current paradigm of topological criticality epitomized by the quantum Hall transitions. We consider models of Chern insulators on…
We study the critical behavior of various geometrical and transport properties of percolation in 6 dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up…
The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition,…
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 study percolative properties of excursion processes and the discrete Gaussian free field (dGFF) in the planar unit disk. We consider discrete excursion clouds, defined using random walks as a two-dimensional version of random…
We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In particular the expected number of clusters separating two pairs of points converges to an explicit…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
The critical properties of the stochastic susceptible-exposed-infected model on a square lattice is studied by numerical simulations and by the use of scaling relations. In the presence of an infected individual, a susceptible becomes…
In this paper, the main focus is on the Sierpinski carpet Julia sets of the rational maps with non-recurrent critical points. We study the uniform quasicircle property of the peripheral circles, the relatively separated property of the…
Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been…
We study the transport properties of directed percolation clusters at the upper critical dimension $d_{c} = 4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field…
The critical behaviour of the Ising model in the absence of an external magnetic field can be specified either through spontaneous symmetry breaking (thermal criticality) or through cluster percolation (geometric criticality). We extend…
It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) procedure based on adding to the functions time and space…
We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling…
Extensive simulations are made of the spin glass susceptibility and correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian and bimodal interaction distributions. Once the transition temperature is accurately…