the relatively few (i.e. 8) disorder realizations we have considered for the two larger sizes, and hence the corresponding large potential error in our estimate of $\Delta T_{\rm m}$, we find our results consistent with the expectation of self averaging.

   $L^2\times L_z$   $[T_{\rm m}]$   $[\Delta E]$   $[\Delta Q]$   $\Delta {T_{\rm m}}\sqrt{V}$   \#
  ----------------- --------------- -------------- -------------- ------------------------------ ----
   $20^2\times 6$       0.2304          0.028          0.057                  0.183               20
                     $\pm$ 0.0009    $\pm$ 0.0005   $\pm$ 0.002                                  
   $30^2\times 6$        0.227          0.026          0.061                  0.190               8
                      $\pm$ 0.001    $\pm$ 0.002    $\pm$ 0.004                                  
   $20^2\times 12$       0.225          0.0279         0.067                  0.184               8
                      $\pm$ 0.001    $\pm$ 0.0004   $\pm$ 0.001                                  

  :  Disorder averaged melting temperature $[T_{\rm m}]$ and discontinuities in the energy per site $[\Delta E]$ and disorder conjugate variable $[\Delta Q]$ for disorder strength $p=0.12$, for different system sizes $L^2\times L_z$. The errors represent the estimated statistical error sampling over the number of independent realizations of the random disorder specified in the last column. $\Delta T_{\rm m}$ is the standard deviation of melting temperatures computed over the independent random realizations, and one expects $\Delta T_{\rm m}\propto 1/\sqrt{V}$, with $V=L^2L_z$ the volume of the system. Results for the $20^2\times 12$ system are computed as described in Sec. \[sIW\].

\[tab1\]

Vortex Glass at Strong 