Crossover behavior for a noninteracting disordered electronic system in the presence of a weak magnetic field

Abstract

Near the noninteracting localization phase transition, we investigate the cross-over between orthogonal and unitary universality classes as a weak magnetic field is applied. We first derive a field-theoretic description of the noninteracting disordered electronic system in the presence of a weak magnetic field. This description contains both symmetries corresponding to the system with and without a magnetic field. We obtain a unified generating functional, from which a variety of relevant physical quantities can be calculated. The theory is then renormalized. The renormalization group flow equations contain information on the fixed points of the theory and on the crossover between the two universality classes. Within ane (=d − 2) expansion the crossover exponent is obtained and previous phenomenological results from the literature are recovered. We also discuss the shift in the location of the mobility edge caused by the weak field.