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

TL;DR

This paper extends the loop algorithm to Heisenberg spin models with spin-ice degeneracy, enabling efficient Monte Carlo simulations to study spin-glass transitions in disordered antiferromagnets with lattice couplings.

Contribution

The authors develop a non-local loop algorithm extension for Heisenberg models, improving simulation capabilities for systems with macroscopic degeneracy.

Findings

Successful application to spin-glass transition study

Overcomes dynamical freezing at low temperatures

Enables efficient simulation of degenerate spin systems

Abstract

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.