Bond dimer percolation on square lattices

Abstract

Percolation due to the simultaneous occupation of two neighboring bond sites, namely a bond dimer, is considered here by means of the renormalization cell technique providing an analytic way to obtain results such as percolation threshold, jamming coverage and critical exponents. This is complementary to previous numerical studies and extends the validation of the renormalization cell technique. Four different bond dimer depositions are considered: nematic, straight, angular and tortuous; results for each of them are given and analyzed separately. Size of the cells is varied. These results are combined with means of finite size scaling to obtain tendencies towards the thermodynamic limit. It is observed that the percolation threshold is reached at lower concentrations than for monomeric bond percolation establishing a trend for correlated bond percolation similar to the one already established for site dimer percolation. Two different techniques are used to obtain the percolation threshold getting results that are in good agreement with numerical simulations; similarly acceptable results for jamming coverage are obtained. Values for critical exponents are also in good agreement with those reported by means of numerical techniques.