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 $z/Rapprox 0.2$ 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).
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