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 p_c 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 p_p^(H,V)(M), second, considering the solution of the equation f(^H,V)(M,p) = p, denoted by p_g^(H,V)(M), and third, using the cross-point of the curves associated to percolation thresholds for horizontal and vertical directions, represented by p_f (M). Critical exponent v is obtained through two different ways: first, using the maximum of the derivative defined as f ' ^(H,V)(M,p_p), and second, considering the cross point of both derivatives f '(M,p_f ). 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.

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