  We describe an ab-initio disordered local moment theory for long period
magnetic phases and investigate the temperature and magnetic field dependence
of the magnetic states in the heavy rare earth elements (HRE), namely
paramagnetic, conical and helical anti-ferromagnetic(HAFM), fan and
ferromagnetic (FM) states. We obtain a generic HRE magnetic phase diagram which
is consequent on the response of the common HRE valence electronic structure to
f-electron magnetic moment ordering. The theory directly links the first order
HAFM-FM transition to the loss of Fermi surface nesting as well as providing a
template for analysing the other phases and exposing where f-electron
correlation effects are particularly intricate. Gadolinium, for a range of
hexagonal, close-packed lattice constants, c and a, is the prototype and
applications to other HREs are made straightforwardly by scaling the pair and
quartic local moment interactions with de Gennes factors and choosing
appropriate lanthanide contracted c and $a$ values.
