1. Jamming and percolation of $k^3$-mers on simple cubic lattices
- Author
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P. M. Centres, A. C. Buchini Labayen, P. M. Pasinetti, and A.J. Ramirez-Pastor
- Subjects
Physics ,Jamming and percolation ,cubic lattices ,Phase transition ,k 3 -mers ,Condensed matter physics ,Statistical Mechanics (cond-mat.stat-mech) ,Ciencias Físicas ,FOS: Physical sciences ,Jamming ,Percolation threshold ,purl.org/becyt/ford/1.3 [https] ,Renormalization group ,Cubic crystal system ,01 natural sciences ,010305 fluids & plasmas ,purl.org/becyt/ford/1 [https] ,Lattice (order) ,0103 physical sciences ,010306 general physics ,Scaling ,Critical exponent ,Condensed Matter - Statistical Mechanics ,CIENCIAS NATURALES Y EXACTAS ,Física de los Materiales Condensados - Abstract
Jamming and percolation of three-dimensional (3D) $k \times k \times k $ cubic objects ($k^3$-mers) deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The $k^3$-mers were irreversibly deposited into the lattice. Jamming coverage $\theta_{j,k}$ was determined for a wide range of $k$ ($2 \leq k \leq 40$). $\theta_{j,k}$ exhibits a decreasing behavior with increasing $k$, being $\theta_{j,k=\infty}=0.4204(9)$ the limit value for large $k^3$-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent $\nu_j$ was measured, being $\nu_j \approx 3/2$. On the other hand, the obtained results for the percolation threshold $\theta_{p,k}$ showed that $\theta_{p,k}$ is an increasing function of $k$ in the range $2 \leq k \leq 16$. For $k \geq 17$, all jammed configurations are non-percolating states, and consequently, the percolation phase transition disappears. The interplay between the percolation and the jamming effects is responsible for the existence of a maximum value of $k$ (in this case, $k = 16$) from which the percolation phase transition no longer occurs. 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., Comment: 26 pages, 9 figures. arXiv admin note: text overlap with arXiv:1905.11438
- Published
- 2019
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