Cluster algorithms for frustrated two dimensional Ising antiferromagnets via dual worm constructions

TL;DR

This paper introduces two dual worm cluster algorithms that enable efficient Monte Carlo simulations of frustrated two-dimensional Ising antiferromagnets, including models on triangular and Kagome lattices, especially in regimes with complex correlations.

Contribution

The paper develops and characterizes two novel dual worm algorithms that improve simulation efficiency for frustrated Ising models with extended interactions.

Findings

Algorithms perform well in regimes with power-law correlations.

One algorithm generalizes to other frustrated systems like Kagome lattices.

Enhanced ergodicity and efficiency in Monte Carlo simulations.

Abstract

We report on the development of two dual worm constructions that lead to cluster algorithms for efficient and ergodic Monte Carlo simulations of frustrated Ising models with arbitrary two-spin interactions that extend up to third-neighbours on the triangular lattice. One of these algorithms generalizes readily to other frustrated systems, such as Ising antiferromagnets on the Kagome lattice with further neighbour couplings. We characterize the performance of both these algorithms in a challenging regime with power-law correlations at finite wavevector.