  We present global solutions of optically thin, two-temperature black hole
accretion disks incorporating magnetic fields. We assume that the
{\pi}{\phi}-component of the Maxwell stress is proportional to the total
pressure, and prescribe the radial dependence of the magnetic flux advection
rate in order to complete the set of basic equations. We obtained magnetically
supported (low-{\beta}) disk solutions, whose luminosity exceeds the maximum
luminosity for an advection-dominated accretion flow (ADAF), L > 0.4 {\alpha}^2
L_Edd, where L_Edd is the Eddington luminosity. The accretion flow is composed
of the outer ADAF, a luminous hot accretion flow (LHAF) inside the transition
layer from the outer ADAF to the low-{\beta} disk, the low-{\beta} disk, and
the inner ADAF. The low-{\beta} disk region becomes wider as the mass-accretion
rate increases further. In the low-{\beta} disk, the magnetic heating balances
the radiative cooling, and the electron temperature decreases from ~ 10^9.5 K
to ~ 10^8 K as the luminosity increases. These results are consistent with the
anti-correlation between the energy cutoff in X-ray spectra (hence the electron
temperature) and the luminosity when L > 0.1 L_Edd, observed in the bright/hard
state during the bright hard-to-soft transitions of transient outbursts in
galactic black hole candidates.
