Discrete holomorphicity and integrability in loop models with open boundaries

作者：de Gier Jan^*; Lee Alexander; Rasmussen Jorgen

来源：Journal of Statistical Mechanics: Theory and Experiment , 2013, P02029.

DOI：10.1088/1742-5468/2013/02/P02029

• integrable spin chains (vertex models)
• loop models and polymers
• rigorous results in statistical mechanics
• solvable lattice models

We consider boundary conditions compatible with discrete holomorphicity for the dilute O(n) and C-2((1)) loop models. In each model, for a general set of boundary plaquettes, multiple types of loop can appear. A generalization of Smirnov's parafermionic observable is therefore required in order to maintain the discrete holomorphicity property in the bulk. We show that there exist natural boundary conditions for this observable which are consistent with integrability, that is to say, that by imposing certain boundary conditions, we obtain a set of linear equations whose solutions also satisfy the corresponding reflection equation. In both loop models, several new sets of integrable weights are found using this approach.

• 出版日期2013-2