  Working with a particular modelization of Ginzburg-Landau phenomenological
theory (see \cite{dutourII}, \cite{dutour} and Section \ref{change-var}), we
first recall the form of the phase diagram of this modelization as it usually
drawn in the physical literature (\cite{tink}, \cite{Kittel}, \cite{sarma} and
\cite{PG-de-Gennes}).
  We then study in detail the special case, when the critical Ginzburg Landau
parameter $k$ is equal to $\frac{1}{\sqrt{2}}$. This allows us to prove that
the critical magnetic field $H_{c1}(k)$ is strictly decreasing at
$k=\frac{1}{\sqrt{2}}$.
  PACS: 01.30.Cc, 02.30.Jr, 74.25.Dw
