Histogram-free multicanonical Monte Carlo sampling to calculate the density of states

We report a new multicanonical Monte Carlo algorithm to obtain the density of states for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain a closed-form expression for the density of states expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical sampling and Wang-Landau sampling. This is enabled by storing the visited states directly and avoiding the explicit collection of a histogram. This practice also has the advantage of avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms.

本研究提出一种新型多正则蒙特卡洛（multicanonical Monte Carlo）算法，用于求解统计力学中具有连续状态变量的物理系统的态密度。相较于该类蒙特卡洛方法（如多正则采样、Wang-Landau采样）的既往变体仅能得到有限分辨率的数值数组，本算法可通过选定基组给出态密度的解析表达式。该优势源于算法直接存储已访问的状态，无需显式构建直方图。此策略还可规避因连续状态变量离散化与分箱操作所导致的不良人工误差。研究结果表明，该方案可在大幅减少蒙特卡洛步数的前提下获得收敛结果，相较现有算法实现了显著的计算加速。