S. Wenzel, S. E. Korshunov, K. Penc, F. Mila
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. The presence of long-ranged correlations is already clear for sizes that can be sampled with local updates, but it is only thanks to the investigation of unusually large systems (containing $\sim 10^8$ spins) with cluster up dates that the system can be proven to consist of equally ordered sublattices. These large-scale simulations have also shown that the scalar chirality exhibits long-range order at zero temperature, implying that the system has to undergo a finite-temperature phase transition. In addition, we provide an improved estimate of the residual entropy of the loop model onto which the ground state manifold can be mapped. 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 where the real space distance between them tends to infinity.
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http://arxiv.org/abs/1305.6418
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