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

For Ising spin models which bear the spin-ice type macroscopic (quasi-)degeneracy, conventional classical Monte Carlo (MC) simulation using single spin flips suffers from dynamical freezing at low temperatures ($T$). A similar difficulty is seen also in a family of Heisenberg spin models with easy-axis anisotropy or biquadratic interactions. In the Ising case, the difficulty is avoided by introducing a non-local update based on the loop algorithm. We present an extension of the loop algorithm to the Heisenberg case. As an example of its application, we review our recent study on spin-glass (SG) transition in a bond-disordered Heisenberg antiferromagnet coupled to local lattice distortions.