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

Abstract

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 ±2π p 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 p − 2 describes this states.1

Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions

“…[73] in connection with the string representation of the 3D Ising model, and further studied in Refs. [74][75][76][77][78]. Following these works, we connect the midpoint of each edge e "forward" to two other midpoints by two vectors ξ e .…”

“…[71,72 is only suitable for single-particle problems, while the approach of Refs. [74][75][76][77][78] is able, in principle, to describe interacting particles. To this end one uses the second quantization, and the scattering matrices at the nodes are "promoted" to R-matrices acting in the Fock spaces attached to edges of the network (see Fig.…”

Characteristics of two-dimensional lattice models from a fermionic realization: Ising andXYZmodels

“…Examples include representation of the R matrix in the Fock space of the scalar fermions and in a space with the basis of fermionic coherent-states, developed in Refs. 26,27,28,30 . These reformulations are fully equivalent, and they allow developing a field theory corresponding to the model.…”

“…The developed theory utilizes the graded R operator formalism 26,27,28,29,30 and allows the generalization to other integrable models, which is demonstrated in this work by operating with rather general R operator.…”

The BaxterQoperator of critical dense polymers

“…Such a conformal field theory is known to be logarithmic, these theories, in contrast with rational CFTs, can be realized by different models for the same value of the central charge and conformal weights. For example Hamiltonian walks on a Manhattan lattice [8,9], the rational triplet theory [10,11,12], symplectic fermions [13,14], the Abelian sanpile model [15], dimers [16], the traveling salesman problem [17] and branching polymers [18] all share the same value of the central charge, which is −2. In this paper we want to continue our analysys [7] of the Logarithmic Minimal Model L 1,2 , also called Critical Dense Polymers [5] in view of the well known works of Bazhanov, Lukyanov and Zamolodchikov [1].…”