Combinatorial aspects of boundary loop models
Combinatorial aspects of boundary loop models
复制标题
边界循环模型的组合方面
DOI：
10.1088/1742-5468/2008/01/p01021
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
H. Saleur
中科院分区：
文献类型：
--
作者：
Jesper Lykke Jacobsen;H. Saleur
我们在本文中讨论组合方面的边界循环模型，即模型的自避免循环上的一条循环得到不同的权重取决于他们是否接触的左，右，两者或没有边界。这些模型的代数描述的Temperley-Lieb代数的推广，被称为双边界TL代数。我们给TL表示的尺寸和相应的退化的配分函数的结果。我们解释这些结果的融合，并在最近发现的大对称性存在于环路模型，铺平了道路的共形场论性质的分析。最后，我们提出了在所有情况下，包括两个边界的一个，这是最近讨论的de Gier和Nichols的格拉姆矩阵的行列式的图解。
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These models are described algebraically by a generalization of the Temperley–Lieb algebra, dubbed the two-boundary TL algebra. We give results for the dimensions of TL representations and the corresponding degeneracies in the partition functions. We interpret these results in terms of fusion and in the light of the recently uncovered large symmetry present in loop models, paving the way for the analysis of the conformal field theory properties. Finally, we propose conjectures for determinants of Gram matrices in all cases, including the two-boundary one, which has recently been discussed by de Gier and Nichols.
图代数的重整塔和基础：平面图及更多
影响因子：
0.9
作者：
Martin P
通讯作者：
Martin P