  We study the low-energy asymptotics of the half-filled Hubbard model with a
circular Fermi surface in $d=1+\epsilon$ continuous dimensions, based on the
one-loop renormalization-group (RG) method. Peculiarity of the $d=1+\epsilon$
dimensions is incorporated through the mathematica structure of the elementary
particle-partcile (PP) and particle-hole (PH) loops: infrared logarithmic
singularity of the PH loop is smeared for $\epsilon>0$. The RG flows indicate
that a quantum phase transition (QPT) from a metallic phase to the Mott
insulator phase occurs at a finite on-site Coulomb repulsion $U$ for
$\epsilon>0$. We also discuss effects of randomness.
