Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study

RAMIREZ-PASTOR, ANTONIO JOSE; CENTRES, PAULO; VOGEL, EUGENIO

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2019 vol. 99 p. 1 - 11

1539-3755

Percolation and jamming of k × k square tiles (k2-mers) deposited on square lattices have been studied bynumerical simulations complemented with finite-size scaling theory and exact enumeration of configurationsfor small systems. The k2-mers were irreversibly deposited into square lattices of sizes L × L with L/kranging between 128 and 448 (64 and 224) for jamming (percolation) calculations. Jamming coverage θj,k wasdetermined for a wide range of k values (2 k 100 with many intermediate k values to allow a fine scalinganalysis). θj,k exhibits a decreasing behavior with increasing k, being θj,k=∞ = 0.5623(3) the limit value forlarge k2-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 ≈ 1. On the otherhand, the obtained results for the percolation threshold θc,k showed that θc,k is an increasing function of k inthe range 1 k 3. For k 4, all jammed configurations are nonpercolating states and, consequently, thepercolation phase transition disappears. An explanation for this phenomenon is offered in terms of the rapidincrease with k of the number of surrounding occupied sites needed to reach percolation, which gets larger thanthe sufficient number of occupied sites to define jamming. In the case of k = 2 and 3, the percolation thresholdsare θc,k=2 (∞) = 0.60355(8) and θc,k=3 = 0.63110(9). Our results significantly improve the previously reportedvalues of θNakac,k=2= 0.601(7) and θNakac,k=3= 0.621(6) [Nakamura, Phys. Rev. A 36, 2384 (1987)]. In parallel, acomparison with previous results for jamming on these systems is also done. Finally, a complete analysis ofcritical exponents and universality has been done, showing that the percolation phase transition involved in thesystem has the same universality class as the ordinary random percolation, regardless of the size k considered.