An alternative perspective to observe the critical phenomena of dilaton black holes

Abstract

The critical phenomena of dilaton black holes are probed from a totally different perspective other than the P–v criticality and the q–U criticality discussed in former literature. We investigate not only the two point correlation function but also the entanglement entropy of dilaton black holes. For both the two point correlation function and the entanglement entropy we consider 4times 2times 2=16 cases due to different choices of parameters. The van der Waals-like behavior can be clearly witnessed from all the T–delta L (T–delta S) graphs for q<q_c. Moreover, the effects of dilaton gravity and the spacetime dimensionality on the phase structure of dilaton black holes are disclosed. Furthermore, we discuss the stability of dilaton black holes by applying the analogous specific heat definition and remove the unstable branch by introducing a bar T=T_*. It is shown that the first order phase transition temperature T_* is affected by both alpha and n. The analogous equal area laws for both the T–delta L graph and the T–delta S graph are examined numerically. The relative errors for all cases are small enough so that we can safely conclude that the analogous equal area laws hold for T–delta L (T–delta S) graph of dilaton black holes.