Currents in the dilute O(n=1) model

2015/10/09 by Gyorgy Z. Feher, G. Z. Fehér, Fehér, G. Z. +3 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Boundary (topology) #Boundary value problem #Condensed matter physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Hexagonal lattice #Lattice (music) #Lattice model (finance) #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Monte Carlo method #Percolation (cognitive psychology) #Physics #Quantum many-body systems #Recursion (computer science) #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.1510.02721

published in arXiv (Cornell University) (Cornell University) · 36 pages, 12 figures, v2: changes in main text, added figures, new appendix included

openalex publication_date 2015/10/09 · arxiv created 2018/11/07 · arxiv updated 2018/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The inverse scattering method approach to the quantum Shabat-Mikhailov model
• Spin chains and combinatorics
• Boundary conditions for integrable quantum systems
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• The domain wall partition function for the Izergin-Korepin 19-vertex model at a root of unity

Related

• Lectures on the Spin and Loop O(n) Models
• Percolation and O(1) loop model
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Macroscopic loops in the loop O(n) model at Nienhuis' critical point
• Lectures on the Ising and Potts models on the hypercubic lattice