Percolation phase transition by removal of k 2 -mers from fully occupied lattices

RAMIREZ, L.S.; CENTRES, PAULO; RAMIREZ-PASTOR, ANTONIO JOSE

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2019 vol. 100 p. 1 - 11

1539-3755

Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inversesite percolation by the removal of k × k square tiles (k2-mers) from square lattices. The process starts withan initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the latticeare connected by occupied sites. Then the system is diluted by removing k2-mers of occupied sites from thelattice following a random sequential adsorption mechanism. The process finishes when the jamming state isreached and no more objects can be removed due to the absence of occupied sites clusters of appropriate sizeand shape. The central idea of this paper is based on finding the maximum concentration of occupied sites, pc,k ,for which the connectivity disappears. This particular value of the concentration is called the inverse percolationthreshold and determines a well-defined geometrical phase transition in the system. The results obtained for pc,kshow that the inverse percolation threshold is a decreasing function of k in the range 1 k 4. For k 5,all jammed configurations are percolating states, and consequently, there is no nonpercolating phase. In otherwords, the lattice remains connected even when the highest allowed concentration of removed sites is reached.The jamming exponent νj was measured, being νj = 1 regardless of the size k considered. In addition, theaccurate determination of the critical exponents ν, β, and γ reveals that the percolation phase transition involvedin the system, which occurs for k varying between one and four, has the same universality class as the standardpercolation problem.