Migdal-Kadanoff renormalization of a nonlinear supervector model with hyperbolic symmetry

Abstract

The Migdal-Kadanoff approximation is applied to a nonlinear σ model with fields taking values in a perfectly graded noncompact superspace G/K of rank one. It is shown how to implement the spherical transform for this model space numerically in a controlled manner. The correlation length exponent ν, and the dimensions of a series of G-invariant scaling operators at the fixed point, are computed for 2 < d ⩽ 3. No perturbative instability of the type found by Kravtsov et al. and Wegner is observed.