Site trimer percolation on square lattices

LEBRECHT W.; VOGEL E. E.; VALDÉS J.; RAMIREZ PASTOR A. J.; CENTRES P. M.; GONZALEZ FLORES M.; NIETO F.

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2015 vol. 92

1539-3755

Percolation of site trimers (k-mers with k = 3) is investigated in a detailed way making use of an analytical model based on renormalization techniques in this problem. Results are compared to those obtained here by means of extensive computer simulations. Five different deposition possibilities for site trimers are included according to shape and orientation of the depositing objects. Analytical results for the percolation threshold pc are all close to 0.55, while numerical results show a slight dispersion around this value. A comparison with pc values previously reported for monomers and dimers establishes the tendency of pc to decrease as k increases. Critical exponent ν was also obtained both by analytical and numerical methods. Results for the latter give values very close to the expected value 4/3 showing that this percolation case corresponds to the universality class of random percolation.