Inverse percolation by removing straight rigid rods from square lattices

Abstract

.Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse percolation by removing straight rigid rods from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing straight rigid rods of length k (k-mers) from the surface. The central idea of this paper is based on finding the maximum concentration of occupied sites (minimum concentration of holes) for which connectivity disappears. This particular value of concentration is called the inverse percolation threshold, and determines a well-defined geometrical phase transition in the system. The results, obtained for k ranging from 2 to 256, showed a nonmonotonic size k dependence for the critical concentration, which rapidly decreases for small particle sizes (). Then, it grows for k = 4, 5 and 6, goes through a maximum at k = 7, and finally decreases again and asymptotically converges towards a definite value for large values of k. Percolating and non-percolating phases extend to infinity in the space of the parameter k and, consequently, the model presents percolation transition in all ranges of said value. This finding contrasts with the results obtained in literature for a complementary problem, where straight rigid k-mers are randomly and irreversibly deposited on a square lattice, and the percolation transition only exists for values of k ranging between 1 and approximately . The breaking of particle-hole symmetry, a distinctive characteristic of the k-mers statistics, is the source of this asymmetric behavior. Finally, the accurate determination of critical exponents reveals that the model belongs to the same universality class as random percolation regardless of the value of k considered.