Gillespie Dirk
Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, IL.
J Comput Phys. 2013 Oct 1;250:1-12. doi: 10.1016/j.jcp.2013.05.001.
An algorithm to approximately calculate the partition function (and subsequently ensemble averages) and density of states of lattice spin systems through non-Monte-Carlo random sampling is developed. This algorithm (called the sampling-the-mean algorithm) can be applied to models where the up or down spins at lattice nodes interact to change the spin states of other lattice nodes, especially non-Ising-like models with long-range interactions such as the biological model considered here. Because it is based on the Central Limit Theorem of probability, the sampling-the-mean algorithm also gives estimates of the error in the partition function, ensemble averages, and density of states. Easily implemented parallelization strategies and error minimizing sampling strategies are discussed. The sampling-the-mean method works especially well for relatively small systems, systems with a density of energy states that contains sharp spikes or oscillations, or systems with little knowledge of the density of states.
开发了一种通过非蒙特卡罗随机抽样近似计算晶格自旋系统的配分函数（以及随后的系综平均值）和态密度的算法。该算法（称为抽样平均算法）可应用于晶格节点处的上自旋或下自旋相互作用以改变其他晶格节点自旋状态的模型，特别是具有长程相互作用的非伊辛类模型，例如此处考虑的生物模型。由于它基于概率的中心极限定理，抽样平均算法还给出了配分函数、系综平均值和态密度的误差估计。讨论了易于实现的并行化策略和误差最小化抽样策略。抽样平均方法对于相对较小的系统、具有包含尖锐尖峰或振荡的能态密度的系统或对态密度了解甚少的系统特别有效。
