# Percolation of polyatomic species on a square lattice

@article{Cornette2003PercolationOP, title={Percolation of polyatomic species on a square lattice}, author={Val{\'e}ria Cornette and Antonio Jos{\'e} Ramirez-Pastor and F D Nieto}, journal={The European Physical Journal B - Condensed Matter and Complex Systems}, year={2003}, volume={36}, pages={391-399} }

Abstract.In this paper, the percolation of (a) linear segments of size k and(b) k-mers of different structures and forms deposited on a square lattice have been studied. In the latter case, site and bond percolation have been examined. The analysis of results obtained by using finite size scaling theory is performed in order to test the universality of the problem by determining the numerical values of the critical exponents of the phase transition occurring in the system. It is also determined…

## 63 Citations

### Percolation of polyatomic species on a simple cubic lattice

- Physics
- 2013

In the present paper, the site-percolation problem corresponding to linear k-mers (containing k identical units, each one occupying a lattice site) on a simple cubic lattice has been studied. The…

### Percolation of polyatomic species with the presence of impurities.

- PhysicsThe Journal of chemical physics
- 2006

In this paper, the percolation of linear segments of size k and k-mers of different structures and forms deposited on a square lattice contaminated with previously adsorbed impurities have been studied and the numerical values of the critical exponents were determined.

### Thermal percolation for interacting monomers adsorbed on square lattices

- Physics
- 2005

In this paper the percolation of monomers on a square lattice is studied as the particles interact with either repulsive or attractive energies. By means of a finite-size scaling analysis, the…

### Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

- Materials Science
- 2012

Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length k (k-mers) on two-dimensional square lattices. The…

### Percolation of aligned rigid rods on two-dimensional square lattices.

- Materials SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

The results show that the percolation threshold exhibits a decreasing function when it is plotted as a function of the kmer size, and in the case of aligned kmers, the intersection points of the curves of R(L,k)(p) for different system sizes exhibit nonuniversal critical behavior, varying continuously with changes in the kmers size.

### Jamming and percolation of k2-mers on simple cubic lattices

- PhysicsPhysical review. E
- 2019

A complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolations, regardless of the size k considered.

### Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice

- Mathematics
- 2017

Monte Carlo simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of linear k-mers (also known as rods or needles) on a two-dimensional…

## References

SHOWING 1-10 OF 34 REFERENCES

### Monte Carlo analysis of percolation of line segments on a square lattice.

- PhysicsPhysical review. B, Condensed matter
- 1994

It is strongly suggested that bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice do not belong to the universality class of random site percolation.

### A site-percolation threshold for the diamond lattice with diatomic substitution.

- Materials SciencePhysical review. B, Condensed matter
- 1988

A Monte Carlo analysis is made of site percolation on a diamond lattice occupied by a mixture of monatomic and diatomic constituents that is generated by an algorithm simulating the results of random…

### The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice

- Mathematics
- 1961

### Incipient Spanning Clusters in Square and Cubic Percolation

- Physics
- 2000

The analysis of extensive numerical data for the percolation proba¬bilities of incipient spanning clusters in two dimensional percolation at criticality are presented. We developed an effective code…

### Probability of Incipient Spanning Clusters in Critical Square Bond Percolation

- Physics
- 1997

The probability of simultaneous occurrence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice with free boundaries at the bond percolation threshold…

### Structural ordering of interacting dimers on a square lattice

- Mathematics
- 1993

We study the entropy of dimers on a semi-infinite M*N square lattice (N to infinity ) with lattice interaction energy per dimer mu 1 and nearest-neighbour interaction energy mu 2. Numerical…

### Percolation and Conduction

- Physics
- 1973

Extensions of percolation theory to treat transport are described. Resistor networks, from which resistors are removed at random, provide the natural generalization of the lattice models for which…

### Geometry of random sequential adsorption

- Computer Science
- 1986

P pores in the RSA configuration are introduced and there is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and theseholes, and the hole size distribution is found to be a parabola.