ECMC 2021 Suwa

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Directed worm algorithm

Hidemaro Suwa

Department of Physics, The University of Tokyo, Tokyo (Japan)

Abstract The worm algorithm is a versatile technique in the Markov chain Monte Carlo method for both classical and quantum systems. The algorithm substantially alleviates critical slowing down and reduces the dynamic critical exponents of various classical systems. The worm update can be viewed as a nontrivial two-particle (kink) problem where the diffusivity is a key to efficient sampling. Using the geometric allocation approach to optimize the worm scattering process, we have proposed a directed worm algorithm that significantly improves the computational efficiency----Worm backscattering is averted, and forward scattering is favored [1]. Our approach successfully enhances the diffusivity of the worm head (kink), being approximately 25 times as efficient as the conventional worm update for the simple cubic lattice model. Surprisingly, our algorithm is even more efficient than the Wolff cluster algorithm, one of the best update algorithms. We estimate the dynamic critical exponent of the simple cubic lattice Ising model to be z=0.27 in the worm update. Our approach can be applied to a wide range of physical systems, such as the phi^4 model, the Potts model, the O(n) loop model, lattice QCD, and frustrated spin systems in combination with the dual worm formalism.

[1] Hidemaro Suwa, Phys. Rev. E 103, 013308 (2021)

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