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Revista mexicana de física
Print version ISSN 0035-001X
Abstract
LEBRECHT, W. and VALDES, J.F.. Umbrales de percolación de sitios. Pequeñas celdas bidimensionales asimétricas. Rev. mex. fis. [online]. 2009, vol.55, n.4, pp.307-311. ISSN 0035-001X.
Site percolation thresholds pc and critical exponent v associated to square lattices, triangular lattices and hexagonal lattices are obtained. We consider a methodology consisting in the growth in size of cells for each geometry, denoted for M. A site is occupied with probability p and 1 - p if it is not occupied. Two directions of the plane: horizontal and vertical, through asymmetrical cells are considered for studying site percolation phenomena, so, a percolation functions associated to horizontal or vertical direction, f H(M,p) or f V(M,p) are obtained respectively. Using finite scaling techniques, the critical points at the thermodynamic limit are obtained. Site percolation thresholds are compared through three different ways: first, using the maximum of the derivative of the function f(H,V)(M,p) denoted by pp(H,V)(M), second, considering the solution of the equation f(H,V)(M,p) = p, denoted by pg(H,V)(M), and third, using the cross-point of the curves associated to percolation thresholds for horizontal and vertical directions, represented by pf (M). Critical exponent v is obtained through two different ways: first, using the maximum of the derivative defined as f ' (H,V)(M,pp), and second, considering the cross point of both derivatives f '(M,pf ). The values associated to site percolation thresholds and critical exponent v are in good agreement with the similar ones informed in literature, validating the methodology proposed here.
Keywords : Percolation; percolation threshold; critical exponent.