  Electronic structure Korringa-Kohn-Rostoker calculations for the
$\sigma$-phase in Fe$_{100-x}$V$_x$ were performed in compositional range of
its occurance ($\sim 34 \le x \le \sim 65$). Fe and V magnetic moments and
hyperfine fields were determined for five inequivalent lattice sites in two
models of magnetic structure, namely ferromagnetic FM and so-called
anti-parallel one, APM, dominated by antiferromagnetic coupling. The average
magnetic moments calculated for FM state overestimate the experimental data,
whereas the corresponding quantities computed for APM state, underestimate
them. Such a behavior remains in line with total energy values being similar
for both models. The calculations showed that both average magnetic moments and
hyperfine fields (on Fe and V atoms) vary with a number of Fe atoms in the
nearest neighbor shell, $NN_{Fe}$, starting from critical values of $NN_{Fe}$,
characteristic of each site.
  The calculated hyperfine fields for Fe and V showed an important role of
valence contributions, being strongly dependent on local magnetic moments
arrangements. In the case of Fe, the computed hyperfine fields are
overestimated with respect to the Mossbauer data, while the corresponding
values for V are underestimated with respect to the NMR results. However, the
linear correlation between average magnetic moment and hyperfine fields,
observed experimentally in FeV $\sigma$-phase, can be well reproduced when
combining theoretical results for the two above-mentioned magnetic structure
models.
