Jamming and percolation of $k^2$-mers on simple cubic lattices

Abstract

Jamming and percolation of square objects of size $k\times k$ ($k^2$-mers) isotropically deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The $k^2$-mers were irreversibly deposited into the lattice. Jamming coverage ${\theta }_{j,k}$ was determined for a wide range of $k$ ($2\le k\le 200$). ${\theta }_{j,k}$ exhibits a decreasing behavior with increasing $k$, being ${\theta }_{j,k\to \infty }=0.4285(6)$ the limit value for large $k^2$-mer sizes. On the other hand, the obtained results shows that percolation threshold, ${\theta }_{c,k}$, has a strong dependence on $k$. It is a decreasing function in the range $2\le k\le 18$ with a minimum around $k=18$ and, for $k\ge 18$, it increases smoothly towards a saturation value. Finally, 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 percolation, regardless of the size $k$ considered.

17 pages, 8 figures. arXiv admin note: text overlap with arXiv:1905.11440

References in corpus (7)

• Percolation of linear $k$-mers on square lattice: from isotropic through partially ordered to completely aligned state
• Percolation and jamming of random sequential adsorption samples of large linear $k$-mers on a square lattice
• Jammed systems of oriented needles always percolate on square lattices
• Dynamical percolation transition in the Ising model studied using a pulsed magnetic field
• Jamming and percolation of $k^3$-mers on simple cubic lattices
• Chiral Plaquette Polaron Theory of Cuprate Superconductivity
• Jamming and percolation of parallel squares in single-cluster growth model

Cited by in corpus (3)

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• Jammed systems of oriented dimers always percolate on hypercubic lattices