论文标题
2D ISING模型的平面直方图比较
Flat histogram method comparison on 2D Ising Model
论文作者
论文摘要
我们比较了应用于2D ISING模型的几种扁平图方法的收敛性，包括最近引入的随机近似以及动态更新因子（SAD）方法。我们将此方法与Wang-Landau（WL）方法，WL方法的$ 1/T $变体和标准随机近似Monte Carlo（SAMC）进行了比较。此外，我们考虑了一个程序WL，然后是具有固定权重的“生产运行”，可以完善熵的估计。据我们所知，这项工作是第一个针对其他方法测试这种方法的工作。我们发现，与纯WL相比，WL随后是生产运行\ emph {do}融合到状态的真实密度。其中三种方法稳健地融合：SAD，$ 1/T $ -WL，WL随后进行生产运行。其中，SAD不需要\ emph {先验}对能量范围的知识。这项工作还表明，WL紧随其后的是生产运行优于其他形式的WL，同时确保了千古和详细的平衡。
We compare the convergence of several flat-histogram methods applied to the 2D Ising model, including the recently introduced stochastic approximation with a dynamic update factor (SAD) method. We compare this method with the Wang-Landau (WL) method, the $1/t$ variant of the WL method, and standard stochastic approximation Monte Carlo (SAMC). In addition, we consider a procedure WL followed by a "production run" with fixed weights that refines the estimation of the entropy. To our knowledge, this work is the first to test this approach against other methods. We find that WL followed by a production run \emph{does} converge to the true density of states, in contrast to pure WL. Three of the methods converge robustly: SAD, $1/t$-WL, and WL followed by a production run. Of these, SAD does not require \emph{a priori} knowledge of the energy range. This work also shows that WL followed by a production run performs superior to other forms of WL while ensuring both ergodicity and detailed balance.
