  We study the large 't Hooft coupling expansion of 1/2 BPS Wilson loops in the
anti-symmetric representation in $ \mathcal{N}=4 $ super Yang-Mills (SYM)
theory at the leading order in the 1/N expansion. Via AdS/CFT correspondence,
this expansion corresponds to the $\alpha'$ expansion in bulk type IIB string
theory. We show that this expansion can be systematically computed by using the
low temperature expansion of Fermi distribution function, known as the
Sommerfeld expansion in statistical mechanics. We check numerically that our
expansion agrees with the exact result of anti-symmetric Wilson loops recently
found by Fiol and Torrents.
