Loop algorithm for classical antiferromagnetic Heisenberg models with   biquadratic interactions
  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. 
Hiroshi Shinaoka, Yusuke Tomita, and Yukitoshi Motome
cond-mat.stat-mech