Abstract
We here study directed self-avoiding walks on site diluted square lattice at the percolation threshold by two parameter real space renormalization group method. We found\(v_\parallel ^{p_c } = 1.00\) and\(v_ \bot ^{p_c } = 0.4348\) from cell-to-cell transformation method. This\(v_ \bot ^{p_c } \) value is then compared with the modified Alexander-Orbach formula that\(v_ \bot ^{p_c } = {{d_S } \mathord{\left/ {\vphantom {{d_S } {2d_L }}} \right. \kern-\nulldelimiterspace} {2d_L }}\) whered s is the fracton dimension andd L is the spreading dimension of the infinite directed percolation cluster.
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Roy, A.K., Manna, S.S. Statistics of directed self-avoiding walks on percolation clusters at the percolation threshold. Z. Physik B - Condensed Matter 61, 205–208 (1985). https://doi.org/10.1007/BF01307777
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DOI: https://doi.org/10.1007/BF01307777