1/N Expansion for Critical Exponents of Magnetic Phase Transitions in CP^{N-1} Model at 2<d<4

TL;DR

This paper calculates critical exponents in the CP^{N-1} model across dimensions 2<d<4 using 1/N expansion, revealing large corrections at N=2 in three dimensions and small corrections near four dimensions.

Contribution

It provides a first-order 1/N expansion analysis of critical exponents in the CP^{N-1} model across different dimensions, comparing with renormalization group results.

Findings

Results agree with RG calculations for d=2+psilon.

Large 1/N corrections at N=2 in d=3.

Small corrections at d=4-psilon, insufficient for phase transition description.

Abstract

Critical exponents in the CP^{N-1} model, which describes localized-moment ferro- 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+\epsilon 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-\epsilon the 1/N-corrections are small at any N and insufficient to describe correctly the magnetic phase transition.