Zero-temperature Monte Carlo study of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice

Abstract

We investigate the ground-state properties of the highly degenerate non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice with Monte Carlo simulations. For that purpose, we introduce an Ising pseudospin representation of the ground states, and we use a simple Metropolis algorithm with local updates, as well as a powerful cluster algorithm. At sizes that can be sampled with local updates, the presence of long-range order is surprisingly combined with an algebraic decay of correlations and the complete disordering of the chirality. It is only thanks to the investigation of unusually large systems (containing $\sim 10^8$ spins) with cluster updates that the true asymptotic regime can be reached and that the system can be proven to consist of equivalent (i.e., equally ordered) sublattices. These large-scale simulations also demonstrate that the scalar chirality exhibits long-range order at zero temperature, implying that the system has to undergo a finite-temperature phase transition. Finally, we show that the average distance in the order parameter space, which has the structure of an infinite Cayley tree, remains remarkably small between any pair of points, even in the limit when the real space distance between them tends to infinity.

15 pages, 10 figures

References in corpus (7)

• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Possible ferro-spin nematic order in NiGa2S4
• Competition between two- and three-sublattice ordering for S=1 spins on the square lattice
• Vortex-induced topological transition of the bilinear-biquadratic Heisenberg antiferromagnet on the triangular lattice
• Degeneracy and ordering of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice
• Gauge symmetry and non-abelian topological sectors in a geometrically constrained model on the honeycomb lattice

Cited by in corpus (1)

• Influence of the biquadratic exchange interaction in the classical ground state magnetic response of the antiferromagnetic icosahedron