title: Potential energy landscape of the two-dimensional XY model: higher-index stationary points.
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.
authors.affiliation: Department of Chemistry, The University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom and Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205, USA.
authors.forename: D
authors.initials: D
authors.lastname: Mehta
authors.affiliation: The Department of Applied Mathematics and Theoretical Physics, The University of Cambridge, Clarkson Road, Cambridge CB3 0EH, United Kingdom.
authors.forename: C
authors.initials: C
authors.lastname: Hughes
authors.affiliation: National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa and Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600, South Africa.
authors.forename: M
authors.initials: M
authors.lastname: Kastner
authors.affiliation: University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors.forename: D J
authors.initials: DJ
authors.lastname: Wales