Baek Seung Ki, Mäkelä Harri, Minnhagen Petter, Kim Beom Jun
Integrated Science Laboratory, Umeå University, Umeå, Sweden.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 1):061104. doi: 10.1103/PhysRevE.83.061104. Epub 2011 Jun 6.
The value of the internal energy per spin is independent of the strip width for a certain class of spin systems on two-dimensional infinite strips. It is verified that the Ising model on the kagome lattice belongs to this class through an exact transfer-matrix calculation of the internal energy for the two smallest widths. More generally, one can suggest an upper bound for the critical coupling strength K(c)(q) for the q-state Potts model from exact calculations of the internal energy for the two smallest strip widths. Combining this with the corresponding calculation for the dual lattice and using an exact duality relation enables us to conjecture the critical coupling strengths for the three- and four-state Potts models on the kagome lattice. The values are K(c)(q=3)=1.0565094269290 and K(c)(q=4)=1.1493605872292, and the values can, in principle, be obtained to an arbitrary precision. We discuss the fact that these values are in the middle of earlier approximate results and furthermore differ from earlier conjectures for the exact values.
对于二维无限条带上某类自旋系统，每个自旋的内能值与条带宽度无关。通过对两个最小宽度的内能进行精确转移矩阵计算，验证了 Kagome 晶格上的伊辛模型属于此类。更一般地，从两个最小条带宽度的内能精确计算中，可以为 q 态 Potts 模型的临界耦合强度 K(c)(q)提出一个上限。将此与对偶晶格的相应计算相结合，并使用精确的对偶关系，使我们能够推测 Kagome 晶格上三态和四态 Potts 模型的临界耦合强度。其值为 K(c)(q = 3) = 1.0565094269290 和 K(c)(q = 4) = 1.1493605872292，原则上这些值可以精确到任意精度。我们讨论了这些值处于早期近似结果中间，并且与早期对精确值的推测不同这一事实。
