Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-01-14
JSTAT (2004) P09010
Physics
Condensed Matter
Statistical Mechanics
25 pages, version accepted by JSTAT
Scientific paper
10.1088/1742-5468/2004/09/P09010
Conjectures for analytical expressions for correlations in the dense O$(1)$ loop model on semi infinite square lattices are given. We have obtained these results for four types of boundary conditions. Periodic and reflecting boundary conditions have been considered before. We give many new conjectures for these two cases and review some of the existing results. We also consider boundaries on which loops can end. We call such boundaries ''open''. We have obtained expressions for correlations when both boundaries are open, and one is open and the other one is reflecting. Also, we formulate a conjecture relating the ground state of the model with open boundaries to Fully Packed Loop models on a finite square grid. We also review earlier obtained results about this relation for the three other types of boundary conditions. Finally, we construct a mapping between the ground state of the dense O$(1)$ loop model and the XXZ spin chain for the different types of boundary conditions.
Batchelor Murray T.
de Gier Jan
Mitra Saibal
Nienhuis Bernard
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