An efficient saddle search method for ordered phase transitions involving translational invariance

IF 7.2 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2024-09-19 DOI:10.1016/j.cpc.2024.109381

Gang Cui, Kai Jiang, Tiejun Zhou

引用次数: 0

Abstract

In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS method includes two stages, escaping from the basin and searching for the index-1 generalized saddle point. The NPSS method climbs upward from the generalized local minimum in segments to overcome the challenges of degeneracy. In each segment, an effective ascent direction is ensured by keeping this direction orthogonal to the nullspace of the initial state in this segment. This method can escape the basin quickly and converge to the transition states efficiently. We apply the NPSS method to the phase transitions between crystals, and between crystal and quasicrystal, based on the Landau-Brazovskii and Lifshitz-Petrich free energy functionals. Numerical results show a good performance of the NPSS method.

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涉及平移不变性的有序相变的高效鞍座搜索法

在这项工作中，我们针对一类涉及平移不变性的相变提出了一种高效的空域保留鞍点搜索（NPSS）方法，在这类相变中，临界状态往往是退化的。NPSS 方法包括两个阶段：逃离盆地和搜索索引-1 广义鞍点。NPSS 方法从广义局部最小值分段向上爬升，以克服退化的挑战。在每个分段中，通过保持上升方向与该分段中初始状态的无效空间正交，确保了有效的上升方向。这种方法可以快速逃离盆地，并高效收敛到过渡状态。我们基于 Landau-Brazovskii 和 Lifshitz-Petrich 自由能函数，将 NPSS 方法应用于晶体之间以及晶体与准晶体之间的相变。数值结果表明 NPSS 方法性能良好。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.