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We consider a version of the symmetric Anderson impurity model (compactified)which has a non-Fermi liquid weak coupling regime. We find that in the Majoranafermion representation, perturbation theory can be conveniently developed interms of Pfaffian determinants and we use this formalism to calculate theimpurity free energy, self energies, and vertex functions. In the second-orderperturbation theory, a linear temperature dependence of electrical resistivityis obtained, and the leading corrections to the impurity specific heat arefound to behave as $T\ln T$. The impurity susceptibilities have terms in $\lnT$ to zero, first, and second order, and corrections of $\ln^2 T$ to secondorder as well. The singlet superconducting paired susceptibility at theimpurity site, is found to have second-order corrections $\ln T$, which weinterpret as an indication that a singlet conduction electron pairing resonanceforms at the Fermi level. When the perturbation theory is extended to thirdorder logarithmic divergences are found in the vertex function$\Gamma_{0,1,2,3}(0,0,0,0)$. Multiplicative renormalization-group method isthen used to sum all the leading order logarithmic contributions, giving riseto a new weak-coupling low-temperature energy scale $T_c=\Delta{\rmexp}\left[-\frac{1}{9}\left(\frac{\pi\Delta}{U} \right )^{2}\right]$. Thescaling equation shows the dimensionless coupling constant$\frac{U}{\pi\Delta}$ is increased as the energy scale $\Delta$ reduces. Ourperturbational results can be justified only in the regime $T>T_c$.Comment: 40 pages, 6 figures, Revtex file, to be published in Phy. Rev.

Non-Fermi-liquid theory of a compactified Anderson single-impurity model