Nematic order by thermal disorder in a three-dimensional lattice-spin model with dipolar-like interactions

TL;DR

This study investigates a 3D lattice-spin model with dipolar-like interactions, revealing that nematic order emerges at low temperatures through thermal disorder, despite the ground state lacking nematic order.

Contribution

It demonstrates the emergence of nematic order via order by disorder in a 3D dipolar-like lattice-spin model, supported by Monte Carlo simulations and finite-size scaling.

Findings

Ground state exhibits full orientational order with respect to staggered magnetization.

Nematic order appears at low temperatures through order by disorder.

Monte Carlo simulations characterize the critical behavior of the phase transition.

Abstract

At low temperatures, some lattice spin models with simple ferromagnetic or antiferromagnetic interactions (for example nearest-neighbour interaction being isotropic in spin space on a bipartite three-dimensional lattice) produce orientationally ordered phases exhibiting nematic (second--rank) order, in addition to the primary first-rank one; on the other hand, in the Literature, they have been rather seldom investigated in this respect. Here we study the thermodynamic properties of a three-dimensional model with dipolar-like interaction. Its ground state is found to exhibit full orientational order with respect to a suitably defined staggered magnetization (polarization), but no nematic second-rank order. Extensive Monte Carlo simulations, in conjunction with Finite-Size Scaling analysis have been used for characterizing its critical behaviour; on the other hand, it has been found that nematic order does indeed set in at low temperatures, via a mechanism of order by disorder.