A relation between the freezing temperature ($T^{}_{rm g}$) and the exchange couplings ($J^{}_{ij}$) in metallic spin-glasses is derived, taking the spin-correlations ($G^{}_{ij}$) into account. This approach does not involve a disorder-average. The
expansion of the correlations to first order in $J^{}_{ij}/T^{}_{rm g}$ leads to the molecular-field result from Thouless-Anderson-Palmer. Employing the current theory of the spin-interaction in disordered metals, an equation for $T^{}_{rm g}$ as a function of the concentration of impurities is obtained, which reproduces the available data from {sl Au}Fe, {sl Ag}Mn, and {sl Cu}Mn alloys well.
Alkaline earth mono-silicides ({AE}Si, {AE} $=$ Ca, Sr, Ba) are poor metals and their transport properties are not solely determined by the Zintl anion, in contrast to their Zintl-type composition. Their conducting network is formed by the depopulate
d ${}^{1}_{infty}$[Si$^{2-}$] $pi$-system and {AE}-$d$ states. This justifies the special local coordination of the metal atoms and the planarity of the silicon chains. The low density of carriers seems to be a playground for magnetic instabilities and the triangular prismatic arrangement of {AE} atoms responsible for the observed weak glassy behavior.
In this paper, the general disagreement of the geometrical lyapunov exponent with lyapunov exponent from tangent dynamics is addressed. It is shown in a quite general way that the vector field of geodesic spread $xi^k_G$ is not equivalent to the tang
ent dynamics vector $xi^k_T$ if the parameterization is not affine and that results regarding dynamical stability obtained in the geometrical framework can differ qualitatively from those in the tangent dynamics. It is also proved in a general way that in the case of Jacobi metric -frequently used non affine parameterization-, $xi^k_G$ satisfies differential equations which differ from the equations of the tangent dynamics in terms that produce parametric resonance, therefore, positive exponents for systems in stable regimes.
