Black hole solutions of type IIB supergravity have been previously constructed
that describe the N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation.
The zero temperature limit of these black holes approach a Lifshitz-like scaling
solution in the infrared. We show that these black holes become unstable at low temperature
and we construct a new class of black hole solutions which are thermodynamically
preferred. The phase transition is third order and incorporates a spontaneous breaking of
the SO(6) global symmetry down to SO(4) × SO(2). The critical exponents for the phase
transition are given by (α, β, γ, δ) = (−1, 1, 1, 2) which differ from the standard mean-field
exponents usually seen in holography. At low temperatures the black holes approach a
novel kind of scaling behaviour in the far IR with spatial anisotropy and hyperscaling violation.
We show that the new ground states are thermal insulators in the direction of the
anisotropy.