  We compute the dimensionally regularised four-loop vacuum energy density of
the SU(N_c) gauge + adjoint Higgs theory, in the disordered phase.
``Scalarisation'', or reduction to a small set of master integrals of the type
appearing in scalar field theories, is carried out in d dimensions, employing
general partial integration identities through an algorithm developed by
Laporta, while the remaining scalar integrals are evaluated in d = 3 -
2\epsilon dimensions, by expanding in \epsilon << 1 and evaluating a number of
coefficients. The results have implications for the thermodynamics of finite
temperature QCD, allowing to determine perturbative contributions of orders
O(g^6 ln(1/g)), O(g^6) to the pressure, while the general methods are
applicable also to studies of critical phenomena in QED-like statistical
physics systems.
