Edge excitations of an incompressible fermionic liquid in a staggered magnetic field

Abstract

A model of lattice fermions in 2 + 1-dimensional space is formulated, the critical states of which are lying at the basis of such physical problems, as the 3D Ising Model(3DIM) and the edge excitations in the Hall effect. The action for these exitations coincides with the action of the 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 plateau transitions in the Hall effect, at other values. The model can be formulated also as a loop gas models in 2D, but unlike the O( n) models, where the loop fugacity is real, here we have directed (clockwise and counterclockwise) loops and phase factors e ±2π p q i for them. The line of phase transitions in the parameter space is found and corresponding continuum limits of these models are 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) cosec model with coupling constant k = q p − 2 describes these states.