Related Experiment Video
Updated: Apr 28, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
Potential energy landscape of the two-dimensional XY model: higher-index stationary points
D Mehta1, C Hughes2, M Kastner3
1Department 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.
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.
More Related Videos
06:44Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
11:00Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
Related Concept Videos
Energy Diagrams - II
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The...
One-Degree-of-Freedom System
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
Potential-Energy Criterion for Equilibrium
Energy Diagrams - I
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...
Stability of Equilibrium Configuration: Problem Solving
Problem-solving in the context of the stability of equilibrium configuration...
Force and Potential Energy in Three Dimensions