On the proportion of metric matroids whose Jacobians have nontrivial $\mathbf{p}$-torsion

We study the proportion of metric matroids whose Jacobians have nontrivial $p$-torsion. We establish a correspondence between these Jacobians and the ${\mathbb{F}}_p$-rational points on configuration hypersurfaces, thereby relating their proportions. By counting points over finite fields, we prove that the proportion of these Jacobians is asymptotically equivalent to $1\mathrm{/}p$.