Critical points of the O(n) loop model on the martini and the 3-12 lattices.
Critical points of the O(n) loop model on the martini and the 3-12 lattices.
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马提尼和 3-12 格上的 O(n) 循环模型的临界点。
DOI：
10.1103/physreve.85.062101
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Wenan Guo
中科院分区：
文献类型：
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作者：
Chengxiang Ding;Z. Fu;Wenan Guo
基于Nienhuis [Phys. Rev. Lett.]提出的蜂窝格上的临界点，我们导出了Martini格上O（n）圈模型的临界线随圈权n的变化关系. 49，1062（1982）]。在极限n→0下，我们证明了Martini格上自避行走的连接常数μ=1.7505645579 μ.基于传输矩阵计算的有限尺寸尺度分析也被执行。数值计算结果与理论预测吻合得很好，具有很高的精度.利用类似的数值方法，我们还研究了3-12格点上的O（n）圈模型。我们获得类似的精确协议与巴彻勒[J.统计的临界点。92，1203（1998）]。
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)].