Currents in the dilute $O(n=1)$ model

Abstract

In the framework of an inhomogeneous solvable lattice model, we derive exact expressions for a boundary-to-boundary current on a lattice of finite width. The model we use is the dilute $O(n=1)$ loop model, related to the Izergin-Korepin spin-1 chain and the critical site percolation on the triangular lattice. Our expressions are derived based on solutions of the $q$-Knizhnik-Zamolodchikov equations, and recursion relations.

36 pages, 12 figures, v2: changes in main text, added figures, new appendix included

References in corpus (4)

• On polynomials interpolating between the stationary state of a O(n) model and a Q.H.E. ground state
• Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
• Exact spin quantum Hall current between boundaries of a lattice strip
• The domain wall partition function for the Izergin-Korepin 19-vertex model at a root of unity

Cited by in corpus (2)

• The dilute Temperley-Lieb O($n=1$) loop model on a semi infinite strip: the sum rule
• Renormalization of crossing probabilities in the dilute Potts model