相关论文: Berezinskii-Kosterlitz-Thouless-like percolation t…
We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with…
Anderson localization transitions are usually referred to as quantum phase transitions from delocalized states to localized states in disordered systems. Here we report an unconventional ``Anderson localization transition'' in…
In an artificial 3D percolation nano medium, the clusters filled by the Ising magnets give rise to a topologically nontrivial magnetic structure, leading to new features of the ferromagnetic phase transition without an external magnetic…
Numerical simulations of Diffusion-Limited and Reaction-Limited Cluster-Cluster Aggregation processes of identical particles are performed in a two-dimensional box. It is shown that, for concentrations larger than a characteristic gel…
We present a dynamic Monte Carlo study of the Kosterlitz-Thouless phase transition for the spin-1/2 quantum XY model in two dimensions. The short-time dynamic scaling behaviour is found and the dynamical exponent $\theta$, $z$ and the…
We investigate the phase transition in a non-planar correlated percolation model with long-range dependence, obtained by considering level sets of a Gaussian free field with mass above a given height $h$. The dependence present in the model…
In some systems, the connecting probability (and thus the percolation process) between two sites depends on the geometric distance between them. To understand such process, we propose gravitationally correlated percolation models for…
We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at $J_c$ to $J^*$ in the gapped phase by a value $|J^* - J_c| =…
We study the topology of a random cubical complex associated to Bernoulli site percolation on a cubical grid. We begin by establishing a limit law for homotopy types. More precisely, looking within an expanding window, we define a sequence…
We consider the fractal dimensions d_k of the k-connected part of percolation clusters in two dimensions, generalizing the cluster (k=1) and backbone (k=2) dimensions. The codimensions X_k = 2-d_k describe the asymptotic decay of the…
The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we…
We investigate site percolation on a weighted planar stochastic lattice (WPSL) which is a multifractal and whose dual is a scale-free network. Percolation is typically characterized by percolation threshold $p_c$ and by a set of critical…
The spin structure of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) is a renewed problem because different Monte Carlo (MC) simulation methods predicted different spin orderings. The usual equilibrium simulation…
In recent years, static and dynamic properties of non-$180^\circ$ domain walls in magnetic materials have attracted a great deal of interest. In this paper, spin-reorientation critical dynamics in the two-dimensional XY model is…
The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…
We consider the classical XY model (O(2) nonlinear sigma-model) on a class of lattices with the (fractal) dimensions 1<D<2. The Berezinskii's harmonic approximation suggests that the model undergoes a phase transition in which the low…
Continuous phase transitions in spin systems can be formulated as percolation of suitably defined clusters. We review this equivalence and then discuss how in a similar way, the color deconfinement transition in SU(2) gauge theory can be…
One of the most relevant manifestations of the Beresinskii-Kosterlitz-Thouless transition occurs in quasi-two-dimensional superconducting systems. The experimental advances made in the last decade in the investigation of superconducting…
The study of crossing probabilities - i.e. probabilities of existence of paths crossing rectangles - has been at the heart of the theory of two-dimensional percolation since its beginning. They may be used to prove a number of results on…
Conduction in bulk polycrystalline high-T$_c$ superconductors with relatively high critical currents has been shown to be percolative. This phenomenon is due to weak links at grain boundaries. These weak links are the major limiting factor…