  Anisotropic interparticle correlations in the simple cubic lattice of
single-domain ferroparticles (SCLF) are studied using both theory and computer
simulation. The theory is based on the Helmholtz free energy expansion like
classical virial series up to the second virial coefficient. The analytical
formula for the Helmholtz free energy is incorporated in a logarithmic form to
minimize the effects of series truncation. The new theoretical approach,
including discrete summation over lattice nodes coordinates, is compared
critically against the classical virial expansion of the Helmholtz free energy
for the dipolar hard sphere fluid; the main differences between the Helmholtz
free energy of SCLF and dipolar hard sphere fluid are discussed. The
theoretical results for the Helmholtz free energy, the magnetization, and the
initial magnetic susceptibility of the SCLF are compared against Molecular
Dynamic simulation data. In all cases, theoretical predictions using
logarithmic form of the Helmholtz free energy are seen to be superior, but they
only have an applicability range of the effective dipolar coupling constant
$\lambda_e < 1.5$. For highest values of $\lambda_e$, the structural transition
of the magnetic dipoles in SCLF is observed in Molecular Dynamic simulation. It
has been shown that for $\lambda_e \gtrsim 2$, an antiferromagnetic order
appears in the system.
