We use global magnetohydrodynamic simulations to study the influence of net vertical magnetic fields on the structure of geometrically thin ( H / r \approx 0.05 ) accretion disks in the Newtonian limit . We consider initial mid-plane gas to magnetic pressure ratios \beta _ { 0 } = 1000 , 300 and 100 , spanning the transition between weakly and strongly magnetized accretion regimes . We find that magnetic pressure is important for the disks ’ vertical structure in all three cases , with accretion occurring at z / R \approx 0.2 in the two most strongly magnetized models . The disk midplane shows outflow rather than accretion . Accretion through the surface layers is driven mainly by stress due to coherent large scale magnetic field rather than by turbulent stress . Equivalent viscosity parameters measured from our simulations show similar dependencies on initial \beta _ { 0 } to those seen in shearing box simulations , though the disk midplane is not magnetic pressure dominated even for the strongest magnetic field case . Winds are present but are not the dominant driver of disk evolution . Over the ( limited ) duration of our simulations , we find evidence that the net flux attains a quasi-steady state at levels that can stably maintain a strongly magnetized disk . We suggest that geometrically thin accretion disks in observed systems may commonly exist in a magnetically ‘ ‘ elevated ’ ’ state , characterized by non-zero but modest vertical magnetic fluxes , with potentially important implications for disk phenomenology in X-ray binaries ( XRBs ) and active galactic nuclei ( AGN ) .