  It is a remarkable property of BCS theory that the ratio of the energy gap at
zero temperature $\Xi$ and the critical temperature $T_c$ is (approximately)
given by a universal constant, independent of the microscopic details of the
fermionic interaction. This universality has rigorously been proven quite
recently in three spatial dimensions and three different limiting regimes: weak
coupling, low density, and high density. The goal of this short note is to
extend the universal behavior to lower dimensions $d=1,2$ and give an exemplary
proof in the weak coupling limit.
