Potential Energy Landscapes for the 2D XY Model: Minima, Transition States and Pathways

Abstract

We describe a numerical study of the potential energy landscape for the two-dimensional XY model (with no disorder), considering up to 100 spins and CPU and GPU implementations of local optimization, focusing on minima and saddles of index one (transition states). We examine both periodic and anti-periodic boundary conditions, and show that the number of stationary points located increases exponentially with increasing lattice size. The corresponding disconnectivity graphs exhibit funneled landscapes; the global minima are readily located because they exhibit relatively large basins of attraction compared to the higher energy minima as the lattice size increases.

16 pages, 6 figures

References in corpus (12)

• Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids
• Exploring the Free Energy Landscape: From Dynamics to Networks and Back
• Phase transitions and configuration space topology
• Tumbling through a landscape: Evidence of instabilities in high-dimensional moduli spaces
• Finding all flux vacua in an explicit example
• Enumerating Gribov copies on the lattice
• Visualizing Basins of Attraction for Different Minimization Algorithms
• Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian
• Coulomb, Landau and Maximally Abelian Gauge Fixing in Lattice QCD with Multi-GPUs
• Energy Landscape of the Finite-Size Mean-field 3-Spin Spherical Model
• Exploring the energy landscape of XY models
• Certifying the Potential Energy Landscape

Cited by in corpus (5)

• Enumerating Copies in the First Gribov Region on the Lattice in up to four Dimensions
• Potential Energy Landscape of the Two-Dimensional XY Model: Higher-Index Stationary Points
• Certification and the Potential Energy Landscape
• Gauge-fixing on the Lattice via Orbifolding
• Density of states of the $XY$ model: an energy landscape approach