利用掩蔽自回归流计算仿射变换的三维伊辛模型的临界温度
Computing the Critical Temperature of the Affine-Transformed $D=3$ Ising Model Using Masked Autoregressive Flow
浏览论文内容
中文总结 AI 辅助
本研究为测量面心立方格点上仿射变换伊辛模型的临界温度，对比多直方图法与掩蔽自回归流法，发现后者计算成本扩展性更优，可作为可行替代方案。
中文摘要 AI 辅助
简单伊辛模型为构建和研究格点场论提供了丰富的环境。作为在任意弯曲流形上构建共形场论（CFT）这一持续项目的一部分，本研究开发了测量面心立方（FCC）格点上仿射变换伊辛模型临界温度β_c的方法。该工作的主要挑战在于找到一种计算高效且准确的方法，用于对蒙特卡罗可观测量关于耦合系数和温度进行插值与外推。在此，我们比较了两种此类方法：传统统计方法采用多直方图（MH）方法，而较新的机器学习方法采用掩蔽自回归流（MAF）来估计一组可观测量的潜在概率密度函数。尽管MH方法是专门为插值和外推蒙特卡罗可观测量而设计的，但我们发现MAF是测量β_c的可行替代方案，其计算成本的扩展性更优。此外，我们还阐述了MAF与本工作相关的额外优势，例如在系统体积方面进行外推。
英文摘要
The simple Ising model provides a rich environment to build and study lattice field theories. As part of an ongoing project to construct a conformal field theory (CFT) on an arbitrarily curved manifold, in this work we develop methods to measure the critical temperature $β_c$ of the affine-transformed Ising model on the face-centered cubic (FCC) lattice. The main challenge in this endeavor is finding a computationally efficient and accurate method of interpolating and extrapolating Monte Carlo observables with respect to coupling coefficients and temperature. Herein, we compare two such methods. A traditional statistical approach uses the multiple histogram (MH) method, while a newer machine learning approach uses a masked autoregressive flow (MAF) to estimate the underlying probability density function of a set of observables. While the MH method is specifically designed to interpolate and extrapolate Monte Carlo observables, we find that MAF is a viable alternative for measuring $β_c$ with a computational cost that scales more favorably. Furthermore, we comment on additional advantages of MAF relevant to our work, such as extrapolating in system volume.
