typical quantities appearing even in the pinning-free case, the pairing entropy density (pair-field propagator) $${\overline {< |\phi_p|^2 >}}=N_v^{-1} \int d^2r {\overline {<
|\psi|^2 >}} \eqno(2.3)$$ and the Abrikosov factor $$\beta_A={{2 \pi} \over h} N_v \biggl( \int d^2r {\overline {<
|\psi|^2 >}} \biggr)^{-2} {\int d^2r {\overline {< |\psi|^4 >}}},
\eqno(2.4)$$ where $N_v=L^2/(2 \pi r_B^2)$ is the number of vortices. The former satisfies a Dyson equation $$\mu={{k_{\rm B} T} \over {\overline {< |\phi_p|^2 >}}}=\mu_0 +
\mu \, x \,
(\beta_A - \Delta_{\rm eff}(T) (\beta_A - 1)), \eqno(2.5)$$ where $x=k_{\rm B} T \, b \, h/(2 \pi \xi_0^2 d \mu^2)$, and $\Delta_{\rm eff}(T)=\Delta d \xi_0^2 /k_{\rm B} T b$ is the pinning strength [*relative*]{} to the thermal fluctuation strength. The Abrikosov factor \[30\] is expressed in the form $$\beta_A=1 + N_v^{-1} \sum_{\bf k} v_{\bf k} ( \, 1 - 2\, x \, V_{\bf
k} \, ), \eqno(2.6)$$ where $V_{\bf k}$ is the fully-renormalized four-point vertex corresponding to the bare one $v_{\bf k}$ and also depends on $\Delta_{\rm eff}$. If the freezing to the solid is of first order, a precursor of the positional ordering of vortices (zero points of $\psi$) will appear only in the vicinity of the transiton. Then, sufficiently above the 