Calculation of η up to O(ε²) of Quantum Heisenberg Antiferromagnet in 1+ε Dimension

Abstract

The isotropic quantum Heisenberg antiferromagnet at T=0 is studied using the renormalization group method for perturbation expansion of the Dyson-Maleev spin wave model in the inverse of the spin size S. The exponent η which characterizes the correlations as ⟨s(r)s(0)⟩∼(1⁄r)^d−1+η is given in powers of ε as η\simeq−2ε². The result does not agree with that of now-linear σ-model in two dimension.