over only those configurations in Fig. \[f3\]a which have $\Delta S/S_0<0.1$. We see broad diffuse peaks of equal low intensity at both ${\bf K}_1$ and ${\bf K}_2$, indicating that this is the vortex liquid state.

=8.6truecm

In Fig. \[f4\]a we plot the histogram $P(\Delta S)$ of values of $\Delta S$ found in the data of Fig. \[f3\]a. We see two well separated peaks centered at $\Delta S/S_0=0$ and $\Delta S/S_0\simeq 0.55$, representing the vortex liquid and vortex lattice states respectively. We define the melting transition temperature $T_{\rm m}(p)$ to be the temperature at which the area under these two peaks is equal. In this manner, varying $p$ and averaging over $8$ independent realizations of the random disorder, we plot the vortex lattice melting line $T_{\rm m}(p)$ for systems of size $20\times 20\times 6$ as the blue solid curve in Fig. \[f1\]. As $p$ increases, $T_m(p)$ decreases while the slope $|dT_{\rm m}/dp|$ rapidly increases. As $p$ increases towards $p_c\simeq 0.22$, with correspondingly low melting $T_{\rm m}$, a failure to achieve proper equilibration of the system prevents us from continuing to trace out the melting curve to lower temperatures.

Next we demonstrate that, within our model system, melting remains a first order 