固定唯象耦合下协方差优化有限尺寸标度对Monte Carlo估计的改进
Improvement of Monte Carlo estimates with covariance-optimized finite-size scaling at fixed phenomenological coupling
摘要：
在蒙特卡洛数据的有限尺寸标度分析中，我们可以选择保持一个重整化群不变量（也称为唯象耦合）固定在一个给定值，而不是计算固定哈密顿参数下的观测量。在这个方案的有限尺寸标度，我们利用统计协方差的观测值之间的蒙特卡罗模拟，以减少统计误差的临界指数的计算中所涉及的数量。这种方法是通用的，不需要额外的计算时间。这种方法在二维和三维的伊辛模型中得到了证明，其中获得了CPU时间的大增益因子。
英文摘要：
In the finite-size scaling analysis of Monte Carlo data, instead of computing the observables at fixed Hamiltonian parameters, one may choose to keep a renormalization-group invariant quantity, also called phenomenological coupling, fixed at a given value. Within this scheme of finite-size scaling, we exploit the statistical covariance between the observables in a Monte Carlo simulation in order to reduce the statistical errors of the quantities involved in the computation of the critical exponents. This method is general and does not require additional computational time. This approach is demonstrated in the Ising model in two and three dimensions, where large gain factors in CPU time are obtained.
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