Related Experiment Video
Updated: Aug 2, 2026
10:56
Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures
Published on: May 20, 2014
Percolation on two- and three-dimensional lattices
1Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG, Brazil. phlm@fisica.ufgm.br
Summary
This study uses an efficient Monte Carlo algorithm to analyze percolation problems on various lattices. Researchers obtained accurate critical concentration and correlation exponent values, confirming universality in wrapping probabilities.
Area of Science:
- Computational Physics
- Statistical Mechanics
- Materials Science
Background:
- Percolation theory studies the formation of connected clusters in random systems.
- Efficient algorithms are crucial for accurate simulations of complex lattice structures.
- Understanding critical phenomena in disordered materials is essential for various applications.
Purpose of the Study:
- To apply a novel Monte Carlo algorithm for simulating site and bond percolation.
- To determine critical parameters like wrapping probabilities and correlation length exponents.
- To investigate universality in percolation phenomena across different lattice types.
Main Methods:
- Utilized the Newman-Ziff Monte Carlo algorithm for high efficiency.
- Simulated site and bond percolation on 2D and 3D lattices (square, simple cubic, HCP, hexagonal).
- Analyzed wrapping probabilities, correlation length critical exponent, and critical concentration.
Main Results:
- Achieved accurate results for critical concentration and correlation length exponent with small systems.
- Obtained reliable wrapping probabilities across diverse lattice structures.
- Confirmed the universal nature of wrapping probabilities in site and bond percolation.
Conclusions:
- The Newman-Ziff algorithm provides an efficient and accurate method for percolation studies.
- Results demonstrate the universality of percolation critical phenomena.
- The study offers valuable insights into the behavior of disordered systems.
Related Concept Videos
02:54Trends in Lattice Energy: Ion Size and Charge
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
02:33Lattice Centering and Coordination Number
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Types of Unit Cells
Imagine taking a large number of identical...
01:18First Law: Particles in Two-dimensional Equilibrium
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Newton's first law tells us about the...
01:25Poisson's And Laplace's Equation
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
01:12Bewley Lattice Diagram
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
01:20Divergence Theorem in 3D Space
In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...