  It is shown that the critical exponent $g_1$ related to pair-connectiveness
and shortest-path (or chemical distance) scaling, recently studied by Porto et
al., Dokholyan et al., and Grassberger, can be found exactly in 2d by using a
crossing-probability result of Cardy, with the outcome $g_1 = 25/24$. This
prediction is consistent with existing simulation results.

Statistical Mechanics;Disordered Systems and Neural Networks