  The two main characteristics of the holmium ions in HoF_3 are that their
local electronic properties are dominated by two singlet states lying well
below the remaining 4f-levels, and that the classical dipole-coupling is an
order of magnitude larger than any other two-ion interactions between the
Ho-moments. This combination makes the system particularly suitable for testing
refinements of the mean-field theory. There are four Ho-ions per unit cell and
the hyperfine coupled electronic and nuclear moments on the Ho-ions order in a
ferrimagnetic structure at T_C=0.53 K. The corrections to the mean-field
behavior of holmium triflouride, both in the paramagnetic and ferrimagnetic
phase, have been calculated to first order in the high-density 1/z-expansion.
The effective medium theory, which includes the effects of the single-site
fluctuations, leads to a substantially improved description of the magnetic
properties of HoF_3, in comparison with that based on the mean-field
approximation.
