Table 4.

The exponents describing the structural properties of SAWs embedded in the backbone of critical site percolation clusters in 2D and 3D, obtained using EE calculations [330]. The relation $g_2^r=g_2^{\ell }{d}_{\min }$ does not appear to hold in this case, at least within the accuracy of these EE studies, and the values reported here have been obtained directly from the simulation results. Also, the des Cloizeaux relation, $g_1^r=({\gamma }_1-1)/{\nu }_r$, shows significant departures from the reported numerical results, in particular in 3D. The numerically obtained values of ${\mu }_1$ are, however, consistent with the relation, ${\mu }_1=p_c\mu$ (see Table 1 for $\mu$), with $p_c=0.5927$ (2D), and 0.3116 (3D).

	2D	3D
${\gamma }_1$	1.34(5)	1.29(5)
${\gamma }_0$	1.26(5)	1.19(5)
${\mu }_1$	1.565(5)	1.462(5)
${\mu }_0$	1.456(5)	1.317(5)
${\nu }_{\ell }$	0.890(5)	0.910(5)
${\nu }_r$	0.778(15)	0.66(1)
${\nu }_r={\nu }_{\ell }/d_{\min }$	0.787(10)	0.662(6)
$g_1^{\ell }$	0.45(10)	0.66(15)
$g_1^r$	0.51(10)	0.91(15)
$g_1^r=g_1^{\ell }{d}_{\min }$	0.51(11)	0.91(20)
$g_2^{\ell }$	1.60(16)	1.95(17)
$g_2^r$	1.26(40)	2.96(18)
${\delta }_{\ell }$	9.5(5)	12.0(5)
${\delta }_r$	4.85(20)	3.10(20)