Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, USA.
J Chem Phys. 2013 Nov 21;139(19):194503. doi: 10.1063/1.4830400.
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 central processing unit and graphics processing unit 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.
我们描述了一个对二维 XY 模型（无无序）的位能景观的数值研究，考虑了多达 100 个自旋和中央处理器和图形处理单元的局部优化实现，重点是指数为 1（过渡态）的极小值和鞍点。我们考察了周期和反周期边界条件，并表明随着晶格尺寸的增加，所定位的稳定点数量呈指数增长。相应的不连续图表现出漏斗状的景观；全局最小值很容易被找到，因为随着晶格尺寸的增加，与更高能量的最小值相比，它们具有相对较大的吸引盆地。
