We use a Langevin dynamics approach to map out the thermal phases of an antiferromagnetic Mott insulator pushed out of equilibrium by a large voltage bias. The Mott insulator is realised in the half-filled Hubbard model in a three dimensional bar geometry with leads at voltage $pm V/2$ connected at the two ends. We decouple the strong Hubbard interaction via the combination of an auxiliary vector field, to capture magnetic fluctuations, and a homogeneous scalar field to maintain half-filling. The magnetic fluctuations are assumed to be slow on electronic timescales. At zero temperature our method reduces to Keldysh mean field theory and yields a voltage driven insulator-metal transition with hysteresis. The Langevin scheme generalises this, allowing us to study the finite temperature nonequilibrium steady state. We find an initially slow and then progressively rapid suppression of the Neel temperature $T_{N}$ and pseudogap temperature $T_{pg}$ with bias, and discover that the bias leads to a finite temperature insulator-metal transition. We explain the thermal results in terms of strong amplitude fluctuation of the local moments in the first order landscape.
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