On the critical phenomena and thermodynamics of charged topological dilaton AdS black holes

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In this paper, we study the phase structure and equilibrium state space geometry of charged topological dilaton black holes in $(n+1)$-dimensional anti-de Sitter spacetime.

• By considering the pairs of parameters $(P\sim V)$ and $(Q\sim U)$ as variables, we analyze the phase structure and critical phenomena of black holes and discuss the relation between the two kinds of critical phenomena.
• We find that the phase structures and critical phenomena drastically depend on the cosmological constant $l$ (or the static electric charge $Q$ of the black holes), dimensionality $n$ and dilaton field $\Phi $.