Inverse percolation by removing straight rigid rods from square lattices

L.S. RAMIREZ; P. M. CENTRES; A. J. RAMIREZ-PASTOR

Valdivia

Conferencia; XIX Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics; 2016

Numerical simulations and finite-size scaling analysis have been carried out to study theproblem of inverse percolation by removing straight rigid rods from square lattices [L.S.Ramirez et al. J. Stat. Mech. P09003 (2015)]. The process starts with an initial configuration,where all lattice sites are occupied and, obviously, the opposite sides of the latticeare connected by nearest-neighbor occupied sites. Then, the system is diluted by randomlyremoving straight rigid rods of length k (k-mers) from the surface. The central idea of thispaper is based on finding the maximum concentration of occupied sites (minimum concentrationof holes) for which connectivity disappears. This particular value of concentrationis called the inverse percolation threshold, and determines a well-defined geometrical phasetransition in the system. The results, obtained for k ranging from 2 to 256, showed a nonmonotonicsize k dependence for the critical concentration, which rapidly decreases for smallparticle sizes (1 ≤ k ≤ 3). Then, it grows for k = 4, 5 and 6, goes through a maximum atk = 7, and finally decreases again and asymptotically converges towards a definite value forlarge values of k. Percolating and non-percolating phases extend to infinity in the space ofthe parameter k and, consequently, the model presents percolation transition in all ranges ofsaid value. This finding contrasts with the results obtained in literature for a complementaryproblem, where straight rigid k-mers are randomly and irreversibly deposited on a squarelattice, and the percolation transition only exists for values of k ranging between 1 andapproximately 1.2×104. The breaking of particle-hole symmetry, a distinctive characteristicof the k-mers statistics, is the source of this asymmetric behavior. Finally, the accuratedetermination of critical exponents reveals that the model belongs to the same universalityclass as random percolation regardless of the value of k considered.