monotonically [*decreases*]{} with increasing $\Delta_{\rm eff}$ down to a value $\simeq \Delta^{(p)} h
(\beta_A-1)/(2 \pi \mu^{3/2})$. Namely, the resulting VG transition line is expected to deviate from the first order line to [*lower*]{} temperature with increasing $\Delta_{\rm eff}(T)$ and, in high $\Delta_{\rm eff}(T)$ limit, approach $$B_{\rm VG}^\infty(T) \simeq H_{c2}(0) \biggl({{-\mu_0}
\over {\theta_f(T)}} \biggr)^{3/2} (\Delta^{(p)})^{1/2}. \eqno(2.16)$$ Although this line \[16\] satisfies the LLL scaling $B \sim (T_c(B) -
T)^{3/2}$ as well as the first order line \[34\] in 3D and LLL $$B_m(T) \simeq H_{c2}(0) {{(-\mu_0)^{3/2}} \over {\theta_f(T)}},
\eqno(2.17)$$ the dependences on the (anisotropic) 3D fluctuation strength $\theta_f=b k_{\rm B} T
\sqrt{\Gamma}/\xi_0^3$ of $B_{\rm VG}^\infty$ and $B_m$ are different from each other.

Through the above findings on the glass transition at or below $B_m(T)$, a picture on the phase diagram above a lower critical point $B_{\rm lcp}$ (defined below) of the thermal first order transition is easily obtained \[17\]. First, since most of the above expressions depend not on $\Delta^{(p)}$ but on the relative pinning strength $\Delta_{\rm eff}(T) \propto 1/T$, a cooling along $B_m(T)$ (i.e., an increase of $B$) will imply an effective enhancement of random pinning effect. Further, as mentioned below eq.(2.2), an inclusion of nonzero $\Delta_\Phi$ additionally induces a pinning 