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Critical behavior of charged dilaton black holes in AdS space

We revisit critical behaviour and phase structure of charged anti-deSitter (AdS) dilaton black holes for arbitrary values of dilaton coupling $α$, and realize several novel phase behaviour for this system. We adopt the viewpoint that cosmological constant (pressure) is fixed and treat the charge of the black hole as a thermodynamical variable. We study critical behaviour and phase structure by analyzing the phase diagrams in $T-S$ and $ q-T$ planes. We numerically derive the critical point in terms of $α$ and observe that for $α=1$ and $α\geq \sqrt{3}$, the system does not admit any critical point, while for $0<α<1$, the critical quantities are not significantly affected by $α$. We find that unstable behavior of the Gibbs free energy for $q<q_{c}$ exhibits a \textit{first order} (discontinuous) phase transition between small and large black holes for $0\leqα<1$. For $1<α<\sqrt{3}$ and $q>q_{c}$, however, a novel first order phase transition occurs between small and large black hole, which has not been observed in the previous studies on phase transition of charged AdS black holes.