This is the first in a series of papers devoted to generalisations of statistical loop models. We define a lattice model of webs on the honeycomb lattice, for n ⩾ 2. It is a statistical model of closed, cubic graphs with certain non-local Boltzmann weights that can be computed from spider relations. For n = 2, the model has no branchings and reduces to the well-known O(N) loop model introduced by Nienhuis (Nienhuis 1982 Phys. Rev. Lett. 49 1062). In the general case, we show that the web model possesses a particular point, at q = e^iπ/(n+1), where the partition function is proportional to that of a -symmetric chiral spin model on the dual lattice. Moreover, under this equivalence, the graphs given by the configurations of the web model are in bijection with the domain walls of the spin model. For n = 2, this equivalence reduces to the well-known relation between the Ising and O(1) models. We define as well an open web model on a simply connected domain with a boundary, and discuss in particular the role of defects on the boundary.

这是一系列致力于统计循环模型推广的论文中的第一篇。我们定义了一个蜂窝网格上的网格模型，对于n ⩾ 2。它是一个封闭的三次图的统计模型，具有某些非局部 Boltzmann 权重，可以从蜘蛛关系中计算出来。对于n = 2，该模型没有分支并简化为 Nienhuis 引入的众所周知的O ( N ) 循环模型 (Nienhuis 1982 Phys. Rev. Lett. 49 1062)。在一般情况下，我们表明网络模型拥有一个特定的点，在q = e ^{i π /( n +1)}，其中分配函数与对偶晶格上的对称手性自旋模型的分配函数成正比。此外，在这种等价关系下，网络模型的配置给出的图与自旋模型的畴壁双射。对于n = 2，这种等价性简化为 Ising 和O (1) 模型之间众所周知的关系。我们还在具有边界的简单连接域上定义了一个开放的Web 模型，并特别讨论了缺陷在边界上的作用。