Potential energy landscape of the two-dimensional XY model: Higher-index stationary points
Date
2014-06-12
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
AIP Publishing LLC
Abstract
The application of numerical techniques to the study of energy landscapes of large systems relies on sufficient sampling of the stationary points. Since the number of stationary points is believed to grow exponentially with system size, we can only sample a small fraction. We investigate the interplay between this restricted sample size and the physical features of the potential energy landscape for the two-dimensional XY model in the absence of disorder with up to N = 100 spins. Using an eigenvector-following technique, we numerically compute stationary points with a given Hessian index I for all possible values of I. We investigate the number of stationary points, their energy and index distributions, and other related quantities, with particular focus on the scaling with N. The results are used to test a number of conjectures and approximate analytic results for the general properties of energy landscapes.
Description
CITATION: Metha, D. et al. 2014. Potential energy landscape of the two-dimensional XY model: Higher-index stationary points. Journal of Chemical Physics, 140, 224503, doi:10.1063/1.4880417.
The original publication is available at http://scitation.aip.org/content/aip/journal/jcp
The original publication is available at http://scitation.aip.org/content/aip/journal/jcp
Keywords
Energy landscape, Two-dimensional square lattice, Stationary points
Citation
Metha, D. et al. 2014. Potential energy landscape of the two-dimensional XY model: Higher-index stationary points. Journal of Chemical Physics, 140, 224503, doi:10.1063/1.4880417.