Discrete holomorphicity and integrability in loop models with open boundaries

de Gier, Jan, Lee, Alexander and Rasmussen, Jorgen (2013) Discrete holomorphicity and integrability in loop models with open boundaries. Journal of Statistical Mechanics: Theory and Experiment, 2013 2: P02029.1-P02029.27. doi:10.1088/1742-5468/2013/02/P02029

Author de Gier, Jan
Lee, Alexander
Rasmussen, Jorgen
Title Discrete holomorphicity and integrability in loop models with open boundaries
Journal name Journal of Statistical Mechanics: Theory and Experiment   Check publisher's open access policy
ISSN 1742-5468
Publication date 2013-02
Year available 2013
Sub-type Article (original research)
DOI 10.1088/1742-5468/2013/02/P02029
Volume 2013
Issue 2
Start page P02029.1
End page P02029.27
Total pages 28
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2014
Language eng
Formatted abstract
We consider boundary conditions compatible with discrete holomorphicity for the dilute O(n) and C2 (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.
Keyword Integrable spin chains (vertex models)
Loop models and polymers
Rigorous results in statistical mechanics
Solvable Lattice Models
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 3 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 4 times in Scopus Article | Citations
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