  We (1) construct a one-parameter family of lattice models of interacting
spins; (2) obtain their exact ground states; (3) derive a
statistical-mechanical analogy which relates their ground states to O(n) loop
gases; (4) show that the models are critical for $d\leq \sqrt{2}$, where $d$
parametrizes the models; (5) note that for the special values
$d=2\cos(\pi/(k+2))$, they are related to doubled level-$k$ SU(2) Chern-Simons
theory; (6) conjecture that they are in the universality class of a
non-relativistic SU(2) gauge theory; and (7) show that its one-loop
$\beta$-function vanishes for all values of the coupling constant, implying
that it is also on a critical line.
