Critical behavior of then-vector model for1<n<2

The Migdal-Kadanoff position-space renormalization-group scheme is used to study the critical behavior of the isotropic n-component-vector model in the previously unexplored region, 1<n<2, 1<d<2, of the n-d plane (d is the dimensionality of the space). We find a continuous phase transition at a finite temperature if d≥$d_l$(n). The lower critical dimension $d_l$(n) increases continuously, but nonlinearly from 1 to 2 as n changes from 1 to 2. For $d_l$(n)≤d