  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.
