Ding Chengxiang, Fu Zhe, Guo Wenan
Physics Department, Anhui University of Technology, Maanshan 243002, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):062101. doi: 10.1103/PhysRevE.85.062101. Epub 2012 Jun 19.
We derive the critical line of the O(n) loop model on the martini lattice as a function of the loop weight n basing on the critical points on the honeycomb lattice conjectured by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. In the limit n→0 we prove the connective constant μ=1.7505645579⋯ of self-avoiding walks on the martini lattice. A finite-size scaling analysis based on transfer matrix calculations is also performed. The numerical results coincide with the theoretical predictions with a very high accuracy. Using similar numerical methods, we also study the O(n) loop model on the 3-12 lattice. We obtain similarly precise agreement with the critical points given by Batchelor [J. Stat. Phys. 92, 1203 (1998)].
我们基于Nienhuis [《物理评论快报》49, 1062 (1982)]所推测的蜂窝晶格上的临界点，推导出作为环权重n的函数的马提尼晶格上O(n)环模型的临界线。在n→0的极限情况下，我们证明了马提尼晶格上自回避行走的连接常数μ = 1.7505645579⋯。还基于转移矩阵计算进行了有限尺寸标度分析。数值结果与理论预测高度吻合。使用类似的数值方法，我们还研究了3 - 12晶格上的O(n)环模型。我们得到了与Batchelor [《统计物理杂志》92, 1203 (1998)]给出的临界点同样精确的一致性。
