  In this paper, we shall study the phase transition of non-minimal coupling of
Einstein-Hilbert gravity and electric field of Yang-Mills type 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 in
canonical ensemble. Our investigation shows that only the second order phase
transition behavior is seen in this model. Also, due to the coupling of the
Yang-Mills field and Ricci scalar, there are differences with the phase
transitions of the usual minimal models. We shall show that in the absence of
non-minimal coupling there is no any phase transition.
