CONICET | Buscador de Institutos y Recursos Humanos

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 initialconfiguration, 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 rigidrods 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. Thisparticular 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 anonmonotonic size k dependence for the critical concentration, which rapidly decreases for small particle sizes (1 k  3). Then, it grows for k = 4, 5 and 6, goes through a maximum at k = 7, and finally decreasesagain 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 presentspercolation 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 asquare lattice, and the percolation transition only exists for values of k ranging between 1 and approximately 1.2×104. The breaking of particle-hole symmetry, a distinctive characteristic of the k-mers statistics, isthe 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 kconsidered