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In recent developments, Monte Carlo methods that strategically break detailed balance to manipulate the flow of probabilities have emerged [1]. These methods include optimizing the transition probabilities during state updates. We developed an optimization algorithm designed to minimize the rejection probability and successfully applied it to various statistical mechanical models, such as the Potts model and quantum spin systems [2]. Further, we introduced an algorithm capable of controlling the rejection rate through a single parameter, revealing that reducing the rejection rate leads to an exponential increase in computational efficiency [3]. Another intriguing strategy for breaking detailed balance is the concept of lifting, which expands the state space to introduce probability flow in the enlarged state space. The lifting technique is particularly effective in particle systems, as demonstrated by the event chain Monte Carlo method [4]. In this talk, reviewing these approaches to constructing nonreversible Markov chains, we will present the lifted directed-worm algorithm [5,6] and the multi-replica swap optimization of the replica exchange method (namely, parallel tempering). These probability control nonreversible Markov chains significantly improve the computational efficiency of Monte Carlo sampling.

[1] H. Suwa and S. Todo, Butsuri 77(11) 731-739 (2022).
[2] H. Suwa and S. Todo, Phys. Rev. Lett. 105, 120603 (2010).
[3] H. Suwa, Physica A 633, 129368 (2024).
[4] W. Krauth, Front. Phys. 9:663457 (2021).
[5] H. Suwa, Phys. Rev. E 103, 013308 (2021).
[6] H. Suwa, Phys. Rev. E 106, 055306 (2022).

Model Calculation Seminars – Kawashima Group (u-tokyo.ac.jp)

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