  We have studied a classical antiferromagnet on a garnet lattice by means of
Monte Carlo simulations in an attempt to examine the role of geometrical
frustration in Gadolinium Gallium Garnet, Gd3Ga5O12 (GGG). Low-temperature
specific heat, magnetisation, susceptibility, the autocorrelation function A(t)
and the neutron scattering function S(Q) have been calculated for several
models including different types of magnetic interactions and with the presence
of an external magnetic field applied along the principal symmetry axes. A
model, which includes only nearest-neighbour exchange, J1, neither orders down
to the lowest temperature nor does it show any tendency towards forming a
short-range coplanar spin structure. This model, however, does demonstrate a
magnetic field induced ordering below T ~ 0.01 J1. In order to reproduce the
experimentally observed properties of GGG, the simulated model must include
nearest neighbour exchange interactions and also dipolar forces. The presence
of weak next-to-nearest exchange interactions is found to be insignificant. In
zero field S(Q) exhibits diffuse magnetic scattering around positions in
reciprocal space where antiferromagnetic Bragg peaks appear in an applied
magnetic field.
