Role of infrared divergences in the 1/N expansion of the U=∞ Anderson model

Abstract

The 1/N corrections to the large-N limit of the U= infinity Anderson model are evaluated as gaussian fluctuations about the mean-field theory of previous work, in terms of the complex sigma -field (Coleman boson). The results at T=0 for the magnetic susceptibility chi ₀ and the f occupation n_f are in agreement with those of Rasul and Hewson (1983-4). The result for the linear coefficient of the specific heat gamma is in agreement with an exact relation due to Yoshimori to O(1/N). Fluctuations in the phase of the order parameter Delta produce infrared divergences which force it to vanish as, Delta / Delta ₀ varies as Lambda ^alpha , as the infrared cut off Lambda to 0, with alpha =n_f²/N, restoring the symmetry which was broken in n_f+b⁺b, consistent with this interpretation. The same results for n_f, chi ₀ and gamma are also obtained in polar coordinates for the sigma -field and in the gauge used in the previous work.