A worm algorithm for the fully-packed loop model

TL;DR

This paper introduces a new worm algorithm for simulating the fully-packed loop model on the honeycomb lattice, demonstrating its ergodicity, efficiency, and ability to measure static and dynamic properties.

Contribution

The paper develops and proves the correctness of a novel worm algorithm for the fully-packed loop model, enabling efficient simulation of a complex frustrated system.

Findings

Algorithm correctly simulates the model and is ergodic.

Estimated dynamic exponent z = 0.515(8).

Measured static quantities like loop-length and face-size moments.

Abstract

We present a Markov-chain Monte Carlo algorithm of worm type that correctly simulates the fully-packed loop model on the honeycomb lattice, and we prove that it is ergodic and has uniform stationary distribution. The fully-packed loop model on the honeycomb lattice is equivalent to the zero-temperature triangular-lattice antiferromagnetic Ising model, which is fully frustrated and notoriously difficult to simulate. We test this worm algorithm numerically and estimate the dynamic exponent z = 0.515(8). We also measure several static quantities of interest, including loop-length and face-size moments. It appears numerically that the face-size moments are governed by the magnetic dimension for percolation.