In this paper, we investigate an integrable loop model and its connect
ion with a supersymmetric spin chain. The Bethe ansatz solution allows
us to study some properties of the ground state. When the loop fugaci
ty q lies in the physical regime, we conjecture that the central charg
e is c = q - 1 for q integer < 2. Low-lying excitations are examined,
supporting a superdiffusive behavior for q = 1. We argue that these sy
stems are interesting examples of integrable lattice models realizing
c less than or equal to 0 conformal field theories.