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

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