Critical behavior of the n-vector model for 1<n<2

Abstract

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<2, the low-temperature phase is characterized by a power-law decay of the two-point correlation function with a temperature-independent exponent.