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We report on the development of two dual worm constructions that lead tocluster algorithms for efficient and ergodic Monte Carlo simulations offrustrated Ising models with arbitrary two-spin interactions that extend up tothird-neighbours on the triangular lattice. One of these algorithms generalizesreadily to other frustrated systems, such as Ising antiferromagnets on theKagome lattice with further neighbour couplings. We characterize theperformance of both these algorithms in a challenging regime with power-lawcorrelations at finite wavevector.

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