derivative with respect to the moduli field $\tilde t$ gives rise to the condition,

$$\label{potmint2}
\begin{split}
\frac{\partial V_h}{\partial \tilde t}|_{\tilde s_0,\tilde t_0} = 
&\frac{1}{16 \tilde s_0 \tilde t_0^4 (3+4 \tilde t_0^2 h''[\tilde t_0])^2}((2-\sqrt{3})e^{h[\tilde 
t_0])]}(2(3+\sqrt{3})\tilde s_0^2 f'[\tilde s_0]^2 (-3+2 \tilde t_0 h'[\tilde t_0])\\
&(3+4 \tilde t_0^2 h''[\tilde t_0])^2 + \tilde s_0 f[\tilde s_0] f'[\tilde s_0] (3+4 \tilde t_0^2 h''[\tilde t_0])
(9(11+7 \sqrt{3}+2(1+\sqrt{3})a \tilde t_0) \\
&+2 \tilde t_0 (2(1+\sqrt{3})\tilde t_0 (9+2 a \tilde t_0)h'[\tilde t_0]^2 
- 4(1+\sqrt{3})\tilde t_0^2 h'[\tilde t_0]^3 + 6 (9+5 \sqrt{3})\tilde t_0 h''[\tilde t_0] \\
&-h'[\tilde t_0](3(11+9 \sqrt{3}+4(1+\sqrt{3})a \tilde t_0) + 4(3+\sqrt{3}\tilde t_0^2 h''[\tilde t_0])))\\
&+ (2+\sqrt{3})f[\tilde s_0]^2 (-27 +\tilde t_0 (4 \tilde t_0^2 h'[\tilde t_0]^3 (3+4 \tilde t_0^2 h''[\tilde t_0]) \\
&+12 \tilde t_0 (-6 h''[\tilde t_0]+4 \tilde t_0^2 h''[\tilde t_0]^2-3 \tilde t_0 h''[\tilde t_0])\\
&-16 \tilde t_0 h'[\tilde t_0]^2 (3 +6 \tilde t_0^2 h''[\tilde t_0]+ \tilde t_0^3 h'''[\tilde t_0])
+ 3 h'[\tilde t_0](27+68 \tilde t_0^2 h''[\tilde t_0] + 16 \tilde t_0^3 h'''[\tilde t_0]))))).
\end{split}$$

Results of the calculation of the second derivatives for suitable choices of $f(\tilde{s})$ and $h(\tilde{t})$ indicates that the conditions stated above can be used to yield a stable global minimum for the scalar potential without having any flat direction. In section (5) 