Department of Physics and Astronomy, University of Waterloo, ON, N2L 3G1, Canada.
J Phys Condens Matter. 2011 Apr 27;23(16):164208. doi: 10.1088/0953-8984/23/16/164208. Epub 2011 Apr 6.
We examine the onset of classical topological order in a nearest neighbour kagome ice model. Using Monte Carlo simulations, we characterize the topological sectors of the ground state using a nonlocal cut measure which circumscribes the toroidal geometry of the simulation cell. We demonstrate that simulations which employ global loop updates that are allowed to wind around the periodic boundaries cause the topological sector to fluctuate, while restricted local loop updates freeze the simulation into one topological sector. The freezing into one topological sector can also be observed in the susceptibility of the real magnetic spin vectors projected onto the kagome plane. The ability of the susceptibility to distinguish between fluctuating and non-fluctuating topological sectors should motivate its use as a local probe of topological order in a variety of related systems.
我们研究了最近邻 kagome 冰模型中经典拓扑序的出现。使用蒙特卡罗模拟，我们使用非局部切口测量来描述基态的拓扑区域，该切口测量围绕模拟单元的环形几何形状。我们证明，允许在周期性边界上缠绕的全局环路更新会导致拓扑区域发生波动，而受限的局部环路更新则会将模拟冻结在一个拓扑区域中。在投影到 kagome 平面上的真实磁自旋向量的磁化率中也可以观察到冻结到一个拓扑区域中。磁化率区分波动和非波动拓扑区域的能力应该激励其作为各种相关系统中拓扑序的局部探针的使用。
