模拟结晶膜的改进算法
Improved Algorithms for Simulating Crystalline Membranes
摘要：
晶体膜的物理学，即嵌入在三维空间中的固定连接表面，并具有外部曲率项，是非常丰富的，具有很大的理论意义。为了理解它们的行为，通常使用数值模拟。不幸的是，传统的蒙特卡罗算法遭受非常长的自相关性和临界减慢在更有趣的阶段的模型。本文研究了模拟晶体膜的改进Monte Carlo算法的性能，如混合超松弛法和单网格法，并将它们的性能与传统的Metropolis算法进行了比较。我们发现，虽然超松弛算法不减少临界减速，它给出了一个整体增益的因素15的大都市算法。另一方面，unigrid算法确实将临界减速指数减少到z apprx。1.7.
英文摘要：
The physics of crystalline membranes, i.e. fixed-connectivity surfaces embedded in three dimensions and with an extrinsic curvature term, is very rich and of great theoretical interest. To understand their behavior, numerical simulations are commonly used. Unfortunately, traditional Monte Carlo algorithms suffer from very long auto-correlations and critical slowing down in the more interesting phases of the model. In this paper we study the performance of improved Monte Carlo algorithms for simulating crystalline membrane, such as hybrid overrelaxation and unigrid methods, and compare their performance to the more traditional Metropolis algorithm. We find that although the overrelaxation algorithm does not reduce the critical slowing down, it gives an overall gain of a factor 15 over the Metropolis algorithm. The unigrid algorithm does, on the other hand, reduce the critical slowing down exponent to z apprx. 1.7.
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