# Jamming and percolation for deposition of k^{2}-mers on square lattices: A Monte Carlo simulation study.

@article{RamirezPastor2019JammingAP, title={Jamming and percolation for deposition of k^\{2\}-mers on square lattices: A Monte Carlo simulation study.}, author={Antonio Jos{\'e} Ramirez-Pastor and P. M. Centres and Eugenio E. Vogel and J. F. Vald{\'e}s}, journal={Physical review. E}, year={2019}, volume={99 4-1}, pages={ 042131 } }

Percolation and jamming of k×k square tiles (k^{2}-mers) deposited on square lattices have been studied by numerical simulations complemented with finite-size scaling theory and exact enumeration of configurations for small systems. The k^{2}-mers were irreversibly deposited into square lattices of sizes L×L with L/k ranging between 128 and 448 (64 and 224) for jamming (percolation) calculations. Jamming coverage θ_{j,k} was determined for a wide range of k values (2≤k≤100 with many…

## 13 Citations

### Jamming and percolation of linear k-mers on honeycomb lattices.

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- 2020

The precise determination of the critical exponents ν, β, and γ indicates that the model belongs to the same universality class as 2D standard percolation regardless of the value of k considered.

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

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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.

### Percolation phase transition by removal of k^{2}-mers from fully occupied lattices.

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The central idea of this paper is based on finding the maximum concentration of occupied sites, p_{c,k}, for which the connectivity disappears, called the inverse percolation threshold, which determines a well-defined geometrical phase transition in the system.

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The bilayer model belongs to the same universality class as two-dimensional standard percolation model, and the differences between the results obtained from bilayer and monolayer phases are explained on the basis of the transversal overlaps between rods occurring in the bilayer problem.

### Percolation in two-species antagonistic random sequential adsorption in two dimensions.

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- 2023

We consider two-species random sequential adsorption (RSA) in which species A and B adsorb randomly on a lattice with the restriction that opposite species cannot occupy nearest-neighbor sites. When…

### Random sequential adsorption on Euclidean, fractal, and random lattices.

- Computer SciencePhysical review. E
- 2019

The results obtained for Euclidean, fractal, and random lattices indicate that the quantities derived from the jamming probability W_{L(M)}(θ), such as (dW_{L}/dθ)_{max} and the inverse of the standard deviation Δ_{L), behave asymptotically as M^{1/2}.

### Kinetics of random sequential adsorption of two-dimensional shapes on a one-dimensional line.

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It appears that the kinetics of packing growth can depend on packing size even for very large packings, and is argued that this transition is a finite-size effect that arises for spherocylinders due to the properties of the contact function.

### Jammed systems of oriented dimers always percolate on hypercubic lattices

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Jammed states of the RSA process of nonoverlapping dimers in a hypercubic lattice of arbitrary space dimension D ⩾ 2 are considered and it is shown that each dimer in such a state belongs to a percolating cluster.

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A continuous model is developed which is amenable to analytical solution in the low compression regime, helpful in understanding the scaling properties of both finite and infinite chains.

## 46 References

### Percolation of linear k-mers on a square lattice: from isotropic through partially ordered to completely aligned states.

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

A fitting formula for percolation threshold, p(c) = a/k(α)+blog(10)k+c, where a, b, c, and α are the fitting parameters depending on anisotropy, is proposed and it is predicted that for large k-mers, isotropically placed at the lattice, percolations cannot occur, even at jamming concentration.

### Percolation in random sequential adsorption of extended objects on a triangular lattice.

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

The percolation aspect of random sequential adsorption of extended objects on a triangular lattice is studied by means of Monte Carlo simulations and it is found that thepercolation threshold decreases, while the jamming coverage increases, with the number of components in the mixture.

### Jamming and percolation in random sequential adsorption of extended objects on a triangular lattice with quenched impurities

- Physics
- 2016

Random sequential adsorption (RSA) on a triangular lattice with defects is studied by Monte Carlo simulations. The lattice is initially randomly covered by point-like impurities at a certain…

### 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 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…

### Jamming and percolation of parallel squares in single-cluster growth model

- Mathematics
- 2014

This work studies the jamming and percolation of parallel squares in a single-cluster growth model. The Leath-Alexandrowicz method was used to grow a cluster from an active seed site. The sites of a…

### Percolational and fractal property of random sequential packing patterns in square cellular structures.

- PhysicsPhysical review. A, General physics
- 1987

The percolational and fractal property of the packing patterns are investigated, and it is clarified that the maximum critical percolation length of the packed squares is presented for the insulator-to-metal transition to take place on the random sequential packing textures.

### Random sequential adsorption of partially oriented linear k-mers on a square lattice.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

Investigation of jamming phenomena on a square lattice for two different models of anisotropic random sequential adsorption of linear k-mers found that denser configurations are observed in disordered systems as compared to those of completely ordered systems.

### 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…