Geometric effects on critical behaviours of the Ising model
Geometric effects on critical behaviours of the Ising model
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DOI：
10.1088/0305-4470/39/18/010
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发表时间：
2005-11
期刊：
影响因子：
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通讯作者：
H. Shima;Y. Sakaniwa
中科院分区：
文献类型：
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作者：
H. Shima;Y. Sakaniwa
我们研究了定义在常负曲率曲面上的二维Ising模型的临界行为。有限尺寸标度分析表明，零场磁化率和关联长度的临界指数与平面上伊辛晶格模型的临界指数有偏差。此外，当减小边界自旋的影响时，临界指数的值趋向于平均场理论得出的值。这些发现证明，当晶格嵌入在负曲面上时，潜在的几何特征是伊辛模型的临界性质的原因。
We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic susceptibility and the correlation length deviate from those for the Ising lattice model on a flat plane. Furthermore, when reducing the effects of boundary spins, the values of the critical exponents tend to those derived from the mean field theory. These findings evidence that the underlying geometric character is responsible for the critical properties of the Ising model when the lattice is embedded on negatively curved surfaces.