An Inversion-Relaxation Approach for Sampling Stationary Points of Spin Model Hamiltonians

TL;DR

This paper introduces an inversion-relaxation method for efficiently sampling stationary points of complex spin model Hamiltonians, outperforming previous techniques especially for bounded potentials, and effectively finds minima and transition states in unbounded cases.

Contribution

The paper presents a novel inversion-relaxation approach that improves sampling efficiency of stationary points in spin models, applicable to both bounded and unbounded potentials.

Findings

Efficiently finds all stationary points in bounded potentials.

Outperforms previous methods in sampling stationary points.

Effectively identifies minima and transition states in unbounded potentials.

Abstract

Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate how this approach can find all the stationary points for potentials or Hamiltonians bounded from above, which includes a large class of important spin models, and we show that it is far more efficient than previous methods. For potentials unbounded from above, the relaxation part of the method is still efficient in finding minima and transition states, which are usually the primary focus of attention for atomistic systems.