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

TL;DR

This study investigates a three-dimensional lattice-spin model with full-range dipolar interactions, demonstrating the emergence of nematic order at finite temperature through order-by-disorder mechanisms, with results aligning with theoretical and experimental findings.

Contribution

It extends previous work on a truncated dipolar model to the full-range case, proving the existence of finite-temperature nematic order and analyzing critical behavior and degeneracy removal.

Findings

Both models exhibit finite-temperature nematic order via order by disorder.

Ground-state energies differ quantitatively between models.

Critical exponents agree with Renormalization Group and experimental data.

Abstract

In a previous paper [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.