Model (RLPM) consists of $\PartNumb$ particles in a volume $\Volu$ in $\Dime$ dimensions. In order to study elasticity, including bulk deformations, $\Volu$ is allowed to fluctuate under a given pressure $\Pres$. The positions of the particles in this fluctuating volume are denoted by $\{\PartPosi_j\}_{j=1}^{\PartNumb}$. The particles in the RLPM interact via two types of interactions: a repulsive interaction $\VExc$ between all pairs of particles (either direct or mediated via a solvent); and an attractive interaction $\VLink$ between the pairs of particles that are chosen at random to be linked. We take the latter to be a soft link (as opposed to the usual hard constraint of vulcanization theory). Thus, the Hamiltonian can be written as $$\begin{aligned}
\label{EQ:HRLPM}
    H_{\RealDiso} =
    \sum_{1\le i<j\le N}^{\PartNumb}
    \VExc (\PartPosi_i-\PartPosi_j)+
    \sum_{e=1}^{\LinkNumb}
    \VLink \big(\vert \PartPosi_{i_e}-\PartPosi_{j_e}\vert\big) .\end{aligned}$$ The label $e$, which runs from $1$ to the total number of links $M$, indexes the links in a given realization of the quenched disorder, and specifies them via the quenched random variables $M$ and $\{i_{e},j_{e}\}_{e=1}^{M}$.

We take $\VExc$ to be a strong, short-ranged repulsion, which serves to penalize density fluctuations and thus render the system nearly incompressible, as is appropriate for regular or polymeric liquids. As we shall describe in 