奥斯陆模型、超均匀性和淬灭的爱德华-威尔金森模型
The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model
摘要：
我们提出了模拟的1维奥斯陆大米堆模型，在每个站点的临界高度是随机重置后，每次倾倒。我们利用沙堆模型的定态是超均匀的这一事实，得到了尺寸系统$> 10^7$。大多数以前的模拟严重缺陷的重要有限尺寸修正。我们发现，所有的临界指数的值与简单的理性：$ν=4/3$的相关长度指数，$D =9/4$的雪崩团簇的分形维数，和$z=10/7 $的动力学指数一致。此外，我们将超均匀性指数与相关长度指数$ν$联系起来。最后，我们讨论了淬火爱德华-威尔金森（qEW）模型的关系，我们发现，特别是局部粗糙度指数是$α_{\rm loc} = 1$。
英文摘要：
We present simulations of the 1-dimensional Oslo rice pile model in which the critical height at each site is randomly reset after each toppling. We use the fact that the stationary state of this sandpile model is hyperuniform to reach system of sizes $> 10^7$. Most previous simulations were seriously flawed by important finite size corrections. We find that all critical exponents have values consistent with simple rationals: $ν=4/3$ for the correlation length exponent, $D =9/4$ for the fractal dimension of avalanche clusters, and $z=10/7 $ for the dynamical exponent. In addition we relate the hyperuniformity exponent to the correlation length exponent $ν$. Finally we discuss the relationship with the quenched Edwards-Wilkinson (qEW) model, where we find in particular that the local roughness exponent is $α_{\rm loc} = 1$.
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