Nematic order in a simple-cubic lattice-spin model with full-ranged dipolar interactions

\begin{abstract}
In a previous paper
[\href{http://dx.doi.org/10.1103/PhysRevE.90.022506}{
Phys. Rev. E 90, 022506 (2014)}], we had studied
thermodynamic and structural properties of a three--dimensional
simple--cubic
lattice model with dipolar--like interaction, truncated at
nearest--neighbor separation, for which the existence of an ordering
transition at finite temperature had been proven mathematically;
here we extend our investigation addressing the
full--ranged counterpart of the model, for which the critical
behavior had been investigated theoretically and experimentally. In
addition the existence of an
ordering transition at finite temperature had been proven mathematically
as well. Both models
exhibited the same continuously degenerate ground--state
configuration, possessing full orientational order with respect to a
suitably defined staggered magnetization (polarization), but no
nematic second--rank order; in both cases, thermal fluctuations remove
the degeneracy, so that nematic order does set in at low but finite
temperature via a mechanism of order by disorder. On the other hand,
there were recognizable quantitative differences between the two
models as for ground--state energy and critical exponent estimates;
the latter were found to agree with early Renormalization Group
calculations and with experimental results.
\end{abstract}
\pacs{05.50.+q, 64.60.-i, 75.10.Hk}