发表机构
Hefei University of Technology; Monash University（合肥工业大学; 蒙纳士大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用不可逆蒙特卡洛算法精确估计了二维和三维自回避轨迹的临界点，精度大幅提升，并验证了其与自回避行走的标度一致性。
AI 中文摘要
自回避轨迹是自回避行走的一个重要变体。在本工作中，我们采用不可逆马尔可夫链蒙特卡洛算法，并结合可逆的Berretti-Sokal算法进行比较，在具有周期性边界条件的方格和简单立方格上模拟自回避轨迹。基于对展开端到端距离和Binder比率的有限尺寸分析，我们精确估计了简单立方格和方格上的临界点分别为0.206 376 9(2)和0.367 561 1(1)，将先前最佳估计的精度分别提高了500倍和70倍。在简单立方格的估计临界点处，我们数值证明了各种量的临界标度行为以及自回避轨迹和自回避行走的长度分布彼此一致。我们精确的数值结果归因于不可逆算法的效率，该算法相对于可逆算法的优势在自回避轨迹模型中比在自回避行走模型中更为显著。
英文摘要
The self-avoiding trail is an important variant of the self-avoiding walk. In this work, we employ an irreversible Markov chain Monte Carlo algorithm, together with the reversible Berretti-Sokal algorithm for comparison, to simulate self-avoiding trails on the square and simple cubic lattices with periodic boundary conditions. Based on finite-size analyses of the unwrapped end-to-end distance and the Binder ratio, we accurately estimate the critical points on the simple cubic and square lattices to be 0.206\,376\,9(2) and 0.367\,561\,1(1), respectively, improving the precision of previous best estimates by factors of 500 and 70. At the estimated critical point of the simple cubic lattice, we numerically demonstrate that both the critical scaling behaviors of various quantities and the length distributions of self-avoiding trails and walks are consistent with each other. Our accurate numerical results are attributed to the efficiency of the irreversible algorithm, whose advantage over the reversible algorithm is even more pronounced for the self-avoiding trail model than for the self-avoiding walk model.
Comments8 pages, 8 figures
