  We exactly compute the partition function for $U(2)_k\times U(2)_{-k}$ ABJM
theory on $\mathbb S^3$ deformed by mass $m$ and Fayet-Iliopoulos parameter
$\zeta $. For $k=1,2$, the partition function has an infinite number of
Lee-Yang zeros. For general $k$, in the decompactification limit the theory
exhibits a quantum (first-order) phase transition at $m=2\zeta $.
