Loop algorithm for classical antiferromagnetic Heisenberg models with biquadratic interactions

Abstract

Monte Carlo simulation using the standard single-spin flip algorithm often fails to sample over the entire configuration space at low temperatures for frustrated spin systems. A typical example is a class of spin-ice type Ising models. In this case, the difficulty can be avoided by introducing a global-flip algorithm, the loop algorithm. Similar difficulty is encountered in O(3) Heisenberg models in the presence of biquadratic interaction. The loop algorithm, however, is not straightforwardly applied to this case, since the system does not have a priori spin-anisotropy axis for constructing the loops. We propose an extension of the loop algorithm to the bilinear-biquadratic models. The efficiency is tested for three different ways to flip spins on a loop in Monte Carlo simulation. We show that the most efficient method depends on the strength of the biquadratic interaction.

6 pages, 3 figures (accepted for publication in the proceedings of ICFCM)

References in corpus (3)

• Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field
• Spin-glass transition in bond-disordered Heisenberg antiferromagnets coupled with local lattice distortions on a pyrochlore lattice
• Loop algorithm for classical Heisenberg models with spin-ice type degeneracy

Cited by in corpus (4)

• Effect of magnetoelastic coupling on spin-glass behavior in Heisenberg pyrochlore antiferromagnets with bond disorder
• Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores
• A cluster algorithm for Monte Carlo simulations of spin ice
• Extended loop algorithm for pyrochlore Heisenberg spin models with spin-ice type degeneracy: application to spin-glass transition in antiferromagnets coupled to local lattice distortions