  Taking as a probe an SU(2) gauge field with Yang-Mills action in a 3+1
dimensional Lifshitz black hole background, we use the gauge/gravity
correspondence to discuss finite temperature effects in the dual theory defined
on the boundary. In order to test the dependence of results on the anisotropic
scaling exponent z we consider two analytical black hole solutions with z=2 and
z=4. Apart from solving the equations of motion in the bulk using a numerical
approach, we also apply an analytical approximation allowing the determination
of the phase transition character, the critical exponent and the critical
temperature behavior as a function of z.
