Loop algorithm for classical antiferromagnetic Heisenberg models with biquadratic interactions

TL;DR

This paper extends the loop algorithm to classical antiferromagnetic Heisenberg models with biquadratic interactions, improving Monte Carlo sampling efficiency in frustrated spin systems where standard methods struggle.

Contribution

The authors develop an extended loop algorithm applicable to bilinear-biquadratic Heisenberg models, addressing the challenge of constructing loops without a fixed spin-anisotropy axis.

Findings

The extended loop algorithm enhances sampling efficiency.

Different spin-flip methods perform variably depending on biquadratic interaction strength.

The proposed method improves Monte Carlo simulations of frustrated spin systems.

Abstract

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.