Shape-dependent finite-size effect of the critical two-dimensional Ising model on a triangular lattice.
Shape-dependent finite-size effect of the critical two-dimensional Ising model on a triangular lattice.
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DOI：
10.1103/physreve.87.022124
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发表时间：
2012-12
期刊：
影响因子：
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通讯作者：
Xintian Wu;N. Izmailian;Wenan Guo
中科院分区：
文献类型：
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作者：
Xintian Wu;N. Izmailian;Wenan Guo
使用键传播算法，我们研究了有限三角形晶格上的临界二维伊辛模型的有限尺寸行为，自由边界有五种形状：三角形，菱形，梯形，六边形和矩形。计算了临界自由能、内能和比热。自由能的精度达到10（-26）。基于几个有限系统的线性尺寸高达N=2000的精确数据，我们提取的体积，表面和角落部分的自由能，内能，和比热准确。我们证实了共形场理论预测的角落自由能是普遍的，并找到对数修正高阶项的临界自由能的菱形，梯形和六边形系统，这是缺席的三角形和矩形系统。由于边缘平行或垂直于内部能量的键方向的对数边缘校正被发现是相同的，而由于相应的边缘比热的对数边缘校正是不同的。得到了角为π/3、π/2和2π/3时的角内能和角比热，以及高阶修正。与我们以前在正方形晶格的矩形上发现的角内能和角比热[Phys.Rev.E86，041149（2012）]相比，我们得出结论，矩形形状的角内能和角比热不是普适的。
Using a bond-propagation algorithm, we study the finite-size behavior of the critical two-dimensional Ising model on a finite triangular lattice with free boundaries in five shapes: triangular, rhomboid, trapezoid, hexagonal, and rectangular. The critical free energy, internal energy, and specific heat are calculated. The accuracy of the free energy reaches 10(-26). Based on accurate data on several finite systems with linear size up to N=2000, we extract the bulk, surface, and corner parts of the free energy, internal energy, and specific heat accurately. We confirm the conformal field theory prediction that the corner free energy is universal and find logarithmic corrections in higher-order terms in the critical free energy for the rhomboid, trapezoid, and hexagonal systems, which are absent for the triangular and rectangular systems. The logarithmic edge corrections due to edges parallel or perpendicular to the bond directions in the internal energy are found to be identical, while the logarithmic edge corrections due to corresponding edges in the specific heat are different. The corner internal energy and corner specific heat for angles π/3, π/2, and 2π/3 are obtained, as well as higher-order corrections. Comparing with the corner internal energy and corner specific heat we previously found on a rectangle of the square lattice [Phys. Rev. E 86, 041149 (2012)], we conclude that the corner internal energy and corner specific heat for the rectangular shape are not universal.