O(1) loop model with different boundary conditions and symmetry classes of alternating-sign matrices
O(1) loop model with different boundary conditions and symmetry classes of alternating-sign matrices
复制标题
具有不同边界条件和交替符号矩阵对称类的 O(1) 循环模型
DOI：
10.1007/s11232-005-0060-7
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发表时间：
2001
影响因子：
1
通讯作者：
Y. Stroganov
中科院分区：
文献类型：
--
作者：
A. Razumov;Y. Stroganov
这项工作是我们最近的论文中，我们讨论了数值证据表明，具有固定的配对模式的完全包装环模型的状态的数量与具有周期性边界条件和偶数个站点的O（1）环模型的基态矢量的分量相一致。我们给出了两个与不同边界条件相关的新的构造：我们提出并数值验证了具有固定配对模式的完全填充环模型的半圈对称态的数目与O（1）的基态矢量的分量一致循环模型与周期性边界条件和奇数个网站和相应数量的垂直对称状态描述的情况下，开放边界条件和偶数个站点。
This work is a continuation of our recent paper where we discussed numerical evidence that the numbers of the states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the O(1) loop model with periodic boundary conditions and an even number of sites. We give two new conjectures related to different boundary conditions: we suggest and numerically verify that the numbers of the half-turn symmetric states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the O(1) loop model with periodic boundary conditions and an odd number of sites and that the corresponding numbers of the vertically symmetric states describe the case of open boundary conditions and an even number of sites.