Effects of power-law Maxwell field on the Van der Waals like phase transition of higher dimensional dilaton black holes

TL;DR

This paper investigates how power-law Maxwell fields influence the phase transitions of higher-dimensional dilaton black holes, revealing corrections to thermodynamic relations and effects on critical parameters, with critical exponents matching mean field theory.

Contribution

It provides analytical solutions for critical points and explores the impact of power-law Maxwell fields on black hole thermodynamics and phase transitions.

Findings

Critical quantities are affected by the power-law Maxwell field.

The parameter constraint is tighter: $0<\alpha^2<1$.

Critical exponents match those of other AdS black holes.

Abstract

The effects of power-law Maxwell field on the Van der Waals like phase transition of higher-dimensional dilaton black holes are probed in detail. It is shown that the Smarr relation gains corrections due to the effects of both the power-law Maxwell field and the dilaton field while thermodynamic volume is exactly the same as that of Einstein-Maxwell-dilaton black holes. We successfully derive the analytic solutions of critical point and carry out some check to ensure that these critical quantities are positive. It is shown that the constraint on the parameters turns out to be $0<\alpha^2<1$, which is more tighter than that in the non-extended phase space. It is also shown that these critical quantities and the ratio $P_cv_c/T_c$ are affected by the power-law Maxwell field. Moreover, critical exponents are found to coincide with those of other AdS black holes, showing the powerful influence of mean field theory.