Exact Solution of the Six-Vertex Model on a Random Lattice

Details Exact Solution of the Six-Vertex Model on a Random Lattice Exact Solution of the Six-Vertex Model on a Random Lattice

1999-11-04

arxiv.org/abs/hep-th/9911023v4

Nucl.Phys. B575 (2000) 513-534

Physics

High Energy Physics

High Energy Physics - Theory

typos corrected and a figure added in Appendix A

Scientific paper

10.1016/S0550-3213(00)00060-2

We solve exactly the 6-vertex model on a dynamical random lattice, using its representation as a large N matrix model. The model describes a gas of dense nonintersecting oriented loops coupled to the local curvature defects on the lattice. The model can be mapped to the c=1 string theory, compactified at some length depending on the vertex coupling. We give explicit expression for the disk amplitude and evaluate the fractal dimension of its boundary, the average number of loops and the dimensions of the vortex operators, which vary continuously with the vertex coupling.

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