Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics

TL;DR

This paper investigates the thermodynamics and phase transitions of dilaton black holes with nonlinear electrodynamics, revealing universal critical exponents and novel zeroth order phase transitions influenced by dilaton coupling.

Contribution

It introduces the analysis of critical behavior and phase transitions of dilaton black holes with nonlinear electrodynamics, including the discovery of a new zeroth order phase transition.

Findings

Critical exponents are universal and independent of parameters.

Identified a novel zeroth order phase transition due to dilaton-electromagnetic coupling.

Phase transition behavior depends on temperature relative to critical and freeze temperatures.

Abstract

In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. At first, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with Van der Waals liquid-gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show they depend on dilaton coupling constant as well as nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. {Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in case of $T>T_c$, we have no phase transition. When $T=T_c$, the system admits a second order phase transition, while for $T=T_{\rm f}<T_c$ the system experiences a first order transition. Interestingly, for $T_{\rm f}<T<T_c$ we observe a \textit{zeroth order} phase transition in the presence of dilaton field. This novel \textit{zeroth order} phase transition is occurred due to a finite jump in Gibbs free energy which is generated by dilaton-electromagnetic coupling constant, $\alpha$, for a certain range of pressure.}