verify by substituting eq.(2.9) into eq.(2.6) that the $\beta_A$-value does not depend remarkably on $N_{\rm cor}$ at least at low enough $T$. In addition, we note that, at low $T$, eq.(2.5) reduces to the mean field result $${\overline {< < |\psi|^2 > >_{\rm sp}}}=- (b \, \beta_A)^{-1} \,
\mu_0,
\eqno(2.10)$$ where $< \,\,\,\,\,>_{\rm sp}$ denotes space average, and the small O($\Delta_{\rm eff}$) correction to $\beta_A$ was neglected.

Now, let us turn to the glass susceptibility in 2D, which is expressed within LLL in the form $$\chi_{\rm G}=N_v^{-1} ({\overline {< |\phi_p|^2 >}})^{-2} \sum_{p,
p'} {\overline {|< \phi_p \, \phi^*_{p'} >|^2}}. \eqno(2.11)$$ In clean limit, $\chi_G$ is given as a ladder-series of the irreducible vertex represented in Fig.1, i.e., $$\chi_G=1 + I_{\rm irr} + I_{\rm irr}^2 + I_{\rm irr}^3 + \cdot \cdot
\cdot \cdot \cdot, \eqno(2.12)$$ where $$I_{\rm irr}={{\Delta \, h} \over {2 \pi N_v \mu^2}} \sum_{\bf k} \,
v_{\bf k} ( 1 - 2 \, x \, V_{\bf k} )^2. \eqno(2.13)$$ Far above the freezing transition where $V_{\bf k}$ is dominated by the RPA term (2.7), we obtain $I_{\rm irr}
\simeq \Delta_{\rm eff}/2(1 - O(x^{-1}))$. Since this expression is insensitive to $B$, one may conclude the absence \[31\] of 2D glass 