  The model of lattice fermions in 2+1 dimensional space is formulated, the
critical states of which are lying in the basis of such physical problems, as
3D Ising Model(3DIM) and the edge excitations in the Hall effect. The action
for this exitations coincides with the action of so called sign-factor model in
3DIM at one values of its parameters, and represent a model for the edge
excitations, which are responsible for the plato transitions in the Hall
effect, at other values. The model can be formulated also as a loop gas models
in 2D, but unlikely the O(n) models, where the loop fugacity is real, here we
have directed (clochwise and conterclochwise) loops and phase factors $e^{\pm
2\pi {p \over q} i}$ for them. The line of phase transitions in the parametric
space will be found and corresponding continuum limits of this models will be
constructed. It appears, that besides the ordinary critical line, which
separates the dense and diluted phases of the models(like in ordinary O(n)
models), there is a line, which corresponds to the full covering of the space
by curves. The N=2 twisted superconformal models with SU(2)/U(1) coset model
coupling constant $k={q \over p}-2$ describes this states.
