1/Nexpansion for critical exponents of magnetic phase transitions in theCPN−1model for 2<d<4

Critical exponents in the ${\mathit{CP}}^{\mathit{N}\mathrm{-}1}$ model, which describes localized-moment ferromagnets and antiferromagnets (N=2 in the Heisenberg model), are calculated from two-particle Green’s functions to first order in 1/N. For d=2+ɛ the results agree with earlier renormalization group calculations. For d=3 the leading 1/N corrections turn out to be very large at N=2. For d=4-ɛ the 1/N corrections are small at any N and insufficient to describe correctly the magnetic phase transition. © 1996 The American Physical Society.