تقرير
Sweeny dynamics for the random-cluster model with small $Q$
| العنوان: | Sweeny dynamics for the random-cluster model with small $Q$ |
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| المؤلفون: | Peng, Zirui, Elçi, Eren Metin, Deng, Youjin, Hu, Hao |
| المصدر: | Phys. Rev. E 108, 055308 (2023) |
| سنة النشر: | 2023 |
| المجموعة: | Condensed Matter |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics |
| الوصف: | The Sweeny algorithm for the $Q$-state random-cluster model in two dimensions is shown to exhibit a rich mixture of critical dynamical scaling behaviors. As $Q$ decreases, the so-called critical speeding-up for non-local quantities becomes more and more pronounced. However, for some quantity of specific local pattern -- e.g., the number of half faces on the square lattice, we observe that, as $Q \to 0$, the integrated autocorrelation time $\tau$ diverges as $Q^{-\zeta}$, with $\zeta \simeq 1/2$, leading to the non-ergodicity of the Sweeny method for $Q \to 0$. Such $Q$-dependent critical slowing-down, attributed to the peculiar form of the critical bond weight $v=\sqrt{Q}$, can be eliminated by a combination of the Sweeny and the Kawasaki algorithm. Moreover, by classifying the occupied bonds into bridge bonds and backbone bonds, and the empty bonds into internal-perimeter bonds and external-perimeter bonds, one can formulate an improved version of the Sweeny-Kawasaki method such that the autocorrelation time for any quantity is of order $O(1)$. Comment: 10 pages, 8 figures, accepted for publication in Physical Review E |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevE.108.055308 |
| URL الوصول: | http://arxiv.org/abs/2308.00254 |
| رقم الأكسشن: | edsarx.2308.00254 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevE.108.055308 |
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