Jamming and percolation of k 3 -mers on simple cubic lattices

BUCHINI LABAYEN A.C.; CENTRES, PAULO; PASINETTI P. M.; RAMIREZ-PASTOR, ANTONIO JOSE

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2019 vol. 100 p. 1 - 9

1539-3755

Jamming and percolation of three-dimensional (3D) k × k × k cubic objects (k3-mers) deposited on simplecubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. Thek3-mers were irreversibly deposited into the lattice. Jamming coverage θj,k was determined for a wide range ofk (2 k 40). θj,k exhibits a decreasing behavior with increasing k, being θj,k=∞ = 0.4204(9) the limit valuefor large k3-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, andthe corresponding spatial correlation length critical exponent νj was measured, being νj ≈ 3/2. However, theobtained results for the percolation threshold θp,k showed that θp,k is an increasing function of k in the range2 k 16. For k 17, all jammed configurations are nonpercolating states, and consequently, the percolationphase transition disappears. The interplay between the percolation and the jamming effects is responsible forthe existence of a maximum value of k (in this case, k = 16) from which the percolation phase transition nolonger occurs. Finally, a complete analysis of critical exponents and universality has been done, showing that thepercolation phase transition involved in the system has the same universality class as the 3D random percolation,regardless of the size k considered.