For \(Z\), this means the trivial path \(\Gamma=\{\emptyset\}\), while for \(Y\ns_{kl}\) this means finding the shortest length path from \(k\) to \(l\). (If there is no straight line path from \(k\) ...For \(Z\), this means the trivial path \(\Gamma=\{\emptyset\}\), while for \(Y\ns_{kl}\) this means finding the shortest length path from \(k\) to \(l\). (If there is no straight line path from \(k\) to \(l\), there will in general be several such minimizing paths.) Note, however, that the presence of the string between sites \(k\) and \(l\) complicates the analysis of \(g\ns_\Gamma\) for the closed loops, since none of the links of \(\Gamma\) can intersect the string.