Exact conjectured expressions for correlations in the dense O(1) loop model on cylinders

DOI10.1088/1742-5468/2004/10/P10006zbMath1073.82521arXivcond-mat/0407578OpenAlexW3100424066MaRDI QIDQ3160102

Saibal Mitra, Bernard Nienhuis

Publication date: 1 February 2005

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0407578

zbMATH Keywords

correlation functionsintegrable spin chains (vertex models)loop models and polymerspercolation problems (theory)

Mathematics Subject Classification ID

Statistical mechanics of polymers (82D60) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items

Nested closed paths in two-dimensional percolation ⋮ Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder: II. Rotated lattice ⋮ On the weighted enumeration of alternating sign matrices and descending plane partitions ⋮ The exact finite size ground state of the O(n= 1) loop model with open boundaries ⋮ Symmetry classes of alternating sign matrices in a nineteen-vertex model ⋮ The dilute Temperley–Lieb O(n  =  1) loop model on a semi infinite strip: the ground state ⋮ The dilute Temperley–Lieb O(n  =  1) loop model on a semi infinite strip: the sum rule ⋮ On polynomials interpolating between the stationary state of a \(O (n)\) model and a Q.H.E. ground state ⋮ The loop-weight changing operator in the completely packed loop model ⋮ Proof of the Razumov-Stroganov conjecture ⋮ Exact asymptotics of the characteristic polynomial of the symmetric Pascal matrix ⋮ Entanglement, combinatorics and finite-size effects in spin chains ⋮ Fully Packed Loop Models on Finite Geometries ⋮ Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder