格点西格玛模型中拓扑限制测量的解释
Interpretation of topologically restricted measurements in lattice sigma-models
摘要：
我们考虑模型的拓扑部门，和困难与他们的蒙特卡罗模拟。特别是，我们关心的情况下，模拟有一个非常长的自相关时间相对于拓扑电荷。然后，可靠的数值测量是可能的，只有在单一的拓扑扇区。挑战在于将这些受限的测量组合起来，以获得完整结果的近似值，该近似值对应于整个配置集上的正确采样。在某些条件下，这是可能的，它还提供了一个估计的拓扑磁化率chi_t。此外，基于拓扑电荷密度的相关性，即使仅从一个拓扑扇区中的数据评估chi_t也是可行的。在这里，我们提出了这些技术的非线性西格玛模型的框架内的数值试验结果。
英文摘要：
We consider models with topological sectors, and difficulties with their Monte Carlo simulation. In particular we are concerned with the situation where a simulation has an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are possible only within single topological sectors. The challenge is to assemble such restricted measurements to obtain an approximation for the full-fledged result, which corresponds to the correct sampling over the entire set of configurations. Under certain conditions this is possible, and it provides in addition an estimate for the topological susceptibility chi_t. Moreover, the evaluation of chi_t might be feasible even from data in just one topological sector, based on the correlation of the topological charge density. Here we present numerical test results for these techniques in the framework of non-linear sigma-models.
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