10953

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

Dhagash Mehta, Ciaran Hughes, Mario Schrock, David J. Wales
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
J. Chem. Phys. 139, 194503; arXiv:1311.5859 [cond-mat.stat-mech], (22 Nov 2013)

@article{2013arXiv1311.5859M,

   author={Mehta}, D. and {Hughes}, C. and {Schr{"o}ck}, M. and {Wales}, D.~J.},

   title={"{Potential Energy Landscapes for the 2D XY Model: Minima, Transition States and Pathways}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1311.5859},

   primaryClass={"cond-mat.stat-mech"},

   keywords={Condensed Matter – Statistical Mechanics},

   year={2013},

   month={nov},

   adsurl={http://adsabs.harvard.edu/abs/2013arXiv1311.5859M},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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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.
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