Critical behavior of charged dilaton black holes in AdS space

We revisit critical behavior and phase structure of charged anti-deSitter (AdS) dilaton black holes for arbitrary values of dilaton coupling alpha, and realize several novel phase behavior of 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 behavior and phase structure by analyzing the phase diagrams in T - S and q-T planes. We numerically derive the critical point in terms of alpha and observe that for alpha = 1 and alpha >= root 3, the system does not admit any critical point, while for 0 < alpha < 1, the critical quantities are not significantly affected by alpha. We find that unstable behavior of the Helmholtz free energy for q < q(c) exhibits a first order (discontinuous) phase transition between small and large black holes for 0 <= alpha < 1, where q(c) is the value of charge at the critical point. For 1 < alpha < root 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.