Integrable chain models with staggered R-matrices

The technique of construction on Manhattan lattice (ML) the fermionic action for Integrable models is presented. The Sign-Factor of 3D Ising model (SF of 3DIM) and Chalker-Coddington-s phenomenological model (CCM) for the edge excitations in Hall effect are formulated in this way. The second one demonstrates the necessity to consider the inhomogeneous models with staggered R-matrices. The disorder over the U(1) phases is taken into account and staggered Hubbard type of model is obtained. The technique is developed to construct the integrable models with staggered R-matrices. The disorder over the U(1) phases is taken into account and staggered Hubbard type of model is obtained. The technique is developed to construct the integrable models with staggered disposition of R-matrices.