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We carried out three-dimensional global resistive magnetohydrodynamic (MHD)simulations of the cooling instability in optically thin hot black holeaccretion flows by assuming bremsstrahlung cooling. General relativisticeffects are simulated by using the pseudo-Newtonian potential. Coolinginstability grows when the density of the accretion disk becomes sufficientlylarge. We found that as the instability grows the accretion flow changes froman optically thin, hot, gas pressure-supported state (low/hard state) to acooler, magnetically supported, quasi-steady state. During this transition,magnetic pressure exceeds the gas pressure because the disk shrinks in thevertical direction almost conserving the toroidal magnetic flux. Since furthervertical contraction of the disk is suppressed by magnetic pressure, the cooldisk stays in an optically thin, spectrally hard state. In the magneticallysupported disk, the heating rate balances with the radiative cooling rate. Themagnetically supported disk exists for time scale much longer than the thermaltime scale and comparable to the accretion time scale.  We examined the stability of the magnetically supported disk analytically,assuming that the toroidal magnetic flux is conserved, and found it thermallyand secularly stable. Our findings may explain why black hole candidates stayin luminous, X-ray hard state even when their luminosity exceeds the thresholdfor the onset of the cooling instability.

Formation of Magnetically Supported Disks during Hard-to-Soft Transitions in Black Hole Accretion Flows