  We consider 3+1-dimensional gauge theories at finite temperature and a finite
density of charges which couple to a 2+1-dimensional Chern-Simons operator,
giving rise to a theta-term with constant spatial gradient of theta. The
strong-coupling limit of thermal N=4 super-Yang-Mills theory with this kind of
anisotropic deformation has been used in the context of the AdS/CFT
correspondence as a model for strongly coupled anisotropic quark-gluon plasma.
In this paper we work out the thermodynamics and the (nontrivial) phase diagram
in the limit of vanishing gauge coupling and compare with the corresponding
strong-coupling results.
