The Phase Transition of Non-minimal Yang-Mills AdS Black Brane

Abstract

In this paper, we shall study the phase transition of non-minimal Einstein-Hilbert gravity and Yang-Mills term in AdS space-time. We couple the Ricci scalar to the Yang-Mills invariant to obtain a modified theory of gravity. A Black brane solution is introduced up to the first order of the term $RF^{(a)}_{\mu \alpha }F^{(a)\mu \alpha}$ in this model. Then, the phase transition of this solution will be investigated. Our investigations show that both the first and second order phase transitions exist in this model.Comment: 17 Pages, 12 figure