Effects of power-law Maxwell field on the critical phenomena of higher dimensional dilaton black holes

The effects of a power-law Maxwell field on the critical phenomena of higher dimensional dilaton black holes are probed in detail. We successfully derive the analytic solutions of the critical point and carry out some checks to ensure that these critical quantities are positive. It is shown that the constraint on the parameter $\alpha$ describing the strength of the coupling of the electromagnetic field and the scalar field turns out to be $0<{\alpha }^2<1$, which is tighter than that in the nonextended phase space. It is also shown that these critical quantities and the ratio $P_c{v}_c/T_c$ are affected by the power-law Maxwell field. Moreover, critical exponents are found to coincide with those of other anti-de Sitter black holes, showing the powerful influence of mean field theory.

Figure 1

(a) $P$ vs $v$ for $p=2$, $n=7$, $q=b=1$, $\alpha =0.5$; (b) $G$ vs $T$ for $p=2$, $n=7$, $q=b=1$, $\alpha =0.5$.