Localization in a magnetic field: Tight binding model with one-half of a flux quantum per plaquette

The conduction properties of a two-dimensional tight-binding model with on-site disorder and an applied perpendicular magnetic field with precisely one-half of a magnetic flux quantum per plaquette are studied. A continuum hamiltonian is derived which enables the construction of a field theory for the diffusive modes. The field theory is shown to be in the universality class of the O(2n, 2n) O(2n) × (2n)(n → 0) non-linear σ-model implying that all the electronic states are localized. The system is shown to be related, via an analytic continuation, to a system of self-interacting fermions in 1 + 1 dimensions, in the n → 0 limit.