Action formulation of the network model of plateau-plateau transitions in the quantum Hall effect

The Lagrangian (action) formulation of the Chalker-Coddington network model for plateau-plateau transitions in the quantum Hall effect is presented based on a model of fermions hopping on Manhattan lattice (ML). The dimensionless Landauer resistance is considered and its average is calculated over the random U(1) phases with constant distribution on the circle. The Lagrangian of the resultant model on ML is found and the corresponding R matrix is written down. It appeared, that this model is integrable, raising hope to investigate physics of plateau- plateau transitions by the exact method of powerful algebraic Bethe ansatz.