Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk
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 Metr...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/83349 http://hdl.handle.net/10220/42534 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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, v* = 2/d and γ/v* = d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate. |
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