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Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk |
Hao Hu1,2,3,Xiaosong Chen2,Youjin Deng1,2( ) |
1. National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
2. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
3. School of Chemical and Biomedical Engineering, Nanyang Technological University, Singapore 637459, Singapore |
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Abstract We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of the Berretti–Sokal algorithm, which is a variant of the Metropolis–Hastings method. The gained efficiency increases with spatial dimension (D), from approximately 10 times in 2D to approximately 40 times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a linear system with a size up to L= 128, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents, υ*= 2/d and γ/υ*= d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.
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| Keywords
Monte Carlo algorithms
self-avoiding walk
irreversible
balance condition
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Corresponding Author(s):
Youjin Deng
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Issue Date: 19 December 2016
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