Phase transitions of neutral planar hairy AdS black holes

We investigate the phase diagram of a general class of $4$-dimensional exact regular hairy planar black holes. For some particular values of the parameters in the moduli potential, these solutions can be embedded in $ω$-deformed $\mathcal{N}=8$ gauged supergravity. We construct the hairy soliton that is the ground state of the theory and show that there exist first order phase transitions.

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