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It is well known that charged black $Dp$ branes of type II string theoryshare a universal phase structure of van der Waals$-$Maxwell liquid-gas typeexcept $D5$ and $D6$ branes. Interestingly, the phase structure of $D5$ and$D6$ branes can be changed to the universal form with the inclusion ofparticular delocalized charged lower-dimensional branes. For $D5$ branes oneneeds to introduce delocalized $D1$ branes, and for $D6$ branes, one needs tointroduce delocalized $D0$ branes to obtain the universal structure. In aprevious paper [J. High Energy Phys. {\bf 04} (2013) 100] Lu with Wei study thephase structure of black $D6$ branes with the introduction of delocalized $D0$branes in a special case when their charges are equal and the dilaton chargevanishes. In this paper, we look at the phase structure of the black $D6/D0$system with the generic values of the parameters, which makes the analysis moreinvolved but the structure more rich. We also provide reasons why therespective modifications of the phase structures to the universal form for theblack $D5$ and $D6$ branes occur when specific delocalized lower-dimensionalbranes are introduced.

Modification of phase structure of black D6 branes in a canonical ensemble and its origin