Properties of a one-dimensional metallic system in the third-order renormalization-group approximation

A one-dimensional system of electrons with interaction parameters g₁ and g₂ is studied by applying the third-order renormalization-group technique. For g₁>0 our result is essentially the same as that obtained previously in the first-order scaling. For g₁<0 the invariant coupling g^'₁πv-0.87 is considerably weaker than that g^'₁πv=-2 in the second-order renormalization obtained by Menyh\'ard and S\'olyom in the low-frequency limit. The phases of the ground state in the present approximation are the same as those predicted in the second-order renormalization. The critical exponents for response functions which describe various critical fluctuations have also been calculated.