  The phase structure of QCD-like gauge theories with fermions in various
representations is an interesting but generally analytically intractable
problem. One way to ensure weak coupling is to define the theory in a small
finite volume, in this case S^3 x S^1. Genuine phase transitions can then occur
in the large N theory. Here, we use this technique to investigate SU(N) gauge
theory with a number N_f of massive adjoint-valued Majorana fermions having
non-thermal boundary conditions around S^1. For N_f =1 we find a line of
transitions that separate the weak-coupling analogues of the confined and
de-confined phases for which the density of eigenvalues of the Wilson line
transform from the uniform distribution to a gapped distribution. However, the
situation for N_f >1 is much richer and a series of weak-coupling analogues of
partially-confined phases appear which leave unbroken a Z_p subgroup of the
centre symmetry. In these Z_p phases the eigenvalue density has p gaps and they
are separated from the confining phase and from one-another by first order
phase transitions. We show that for small enough mR (the mass of the fermions
times the radius of the S^3) only the confined phase exists. The large N phase
diagram is consistent with the finite N result and with other approaches based
on R^3 x S^1 calculations and lattice simulations.
