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.Comment: 12 pages, 2 figures, contribution to the proceedings of Advanced NATO
Workshop on Statistical Field Theories, Como, June 18-23, 200