the Gibbs factorial factor, which is normally introduced to compensate for the overcounting of identical configuration, is a genuinely subtle one in the context of random solids (for a discussion, see Ref. [@Goldbart1996]). However, our focus will be on observables such as order parameter rather than on free energies, and thus the omission of the Gibbs factor is of no consequence. The factor $$\begin{aligned}
\label{EQ:DeltReal}
    \LinkPote\big( \vert \PartPosi_{i_e} - \PartPosi_{j_e} \vert \big)
    \equiv e^{  -\frac{\vert \PartPosi_{i_e} - \PartPosi_{j_e} \vert^2}
    {2  \LinkScal^2}}\end{aligned}$$ is associated with the link-induced attractive interaction term in the Hamiltonian. The average $\ltha \cdots \rtha_{1}^{\HamiExcl}$, taken with respect to a Boltzmann weight involving the excluded-volume interaction Hamiltonian $\HamiExcl$, is defined as $$\begin{aligned}
    \ltha \cdots \rtha_{1}^{\HamiExcl} \equiv
    \frac{1}{\PartitionLiquid(V)}\int _{\Volu} \prod_{i=1}^{\PartNumb} d \PartPosi_i \,
        e^{-\frac{\HamiExcl}{{\BoltCons}T}}\ldots\, .\end{aligned}$$ The corresponding Helmholtz free energy is then given by $$\begin{aligned}
    \HelmFreeEner _{\RealDiso} (\Volu) \equiv -\BoltCons T \ln Z_{\RealDiso} (\Volu).\end{aligned}$$

To perform the average of the free energy over the quenched disorder, we shall need to choose a probability distribution that assigns a sensible statistical weight $\DEDist (\{ i_e, j_e\}_{e=1}^{\LinkNumb})$ to each possible realization of the total number $\LinkNumb$ and location $\{i_e,j_e\}_{e=1}^{\LinkNumb}$ of the links. Following an elegant strategy due to Deam and Edwards [@Deam1976], 