  Based on the characteristics of the magnetorotational instability (MRI) and
the MRI-driven turbulence, we construct a steady model for a geometrically thin
disk using "non-standard" $\alpha$-prescription. The efficiency of the angular
momentum transport depends on the magnetic Prandtl number, $Pm = \nu/\eta$,
where $\nu$ and $\eta$ are the microscopic viscous and magnetic diffusivities.
In our disk model, Shakura-Sunyaev's $\alpha$-parameter has a power-law
dependence on the magnetic Prandtl number, that is $\alpha \propto Pm^\delta$
where $\delta$ is the constant power-law index. Adopting Spitzer's microscopic
diffusivities, the magnetic Prandtl number becomes a decreasing function of the
disk radius when $\delta > 0$. The transport efficiency of the angular momentum
and the viscous heating rate are thus smaller in the outer part of the disk,
while these are impacted by the size of index $\delta$. We find that the disk
becomes more unstable to the gravitational instability for a larger value of
index $\delta$. The most remarkable feature of our disk model is that the
thermal and secular instabilities can grow in its middle part even if the
radiation pressure is negligibly small in the condition $\delta > 2/3$. In the
realistic disk systems, it would be difficult to maintain the steady mass
accretion state unless the $Pm$-dependence of MRI-driven turbulence is
relatively weak.
