论文标题
二维系统热力学对其表面拓扑类别的敏感性
Sensitivity of the thermodynamics of two-dimensional systems towards the topological classes of their surfaces
论文作者
论文摘要
使用Monte Carlo模拟，我们研究了具有各种拓扑结构的三维，正方形和六角形晶格上的二维ISING模型。我们专注于磁敏感性和平面散装系统临界点附近的特定热量的行为。我们发现，这些数量在球形表面上的缩放函数（Euler特性k = 2）与投射平面上的缩放函数（k = 1）不同，这反过来又与圆环和klein瓶上的缩放函数不同（两个k = 0）。这提供了有力的证据表明，二维表面上伊辛模型的相变取决于它们的拓扑。
Using Monte Carlo simulations we study the two-dimensional Ising model on triangular, square, and hexagonal lattices with various topologies. We focus on the behavior of the magnetic susceptibility and of the specific heat near the critical point of the planar bulk system. We find that scaling functions of these quantities on the spherical surface (Euler characteristic K = 2) differ from the scaling functions on the projective plane (K = 1) which, in turn, differ from the scaling functions on the torus and on the Klein bottle (both K = 0). This provides strong evidence that phase transitions of the Ising model on two-dimensional surfaces depend on their topologies.
