Localization Characteristics of Relativistic vs Nonrelativistic Fermions on a Lattice

Abstract

Relativistic fermions on a lattice are shown to correspond to the $fluctuations$ in the localized nonrelativistic fermions. Therefore, in contrast to nonrelativistic case, the relativistic fermions are critical with universal exponents described by the strong coupling limit of the nonrelativistic problem. The fluctuations also describe $anisotropic$ spin chain at the onset to {\it long range magnetic order} whose universality class is the Ising model. This generalizes the universality in spin models to include multifractal exponents. Finally, analogous to the nonrelativistic case, the relativistic fermions may exhibit ballistic character due to correlations.