We introduce a two dimensional nonlinear XY model with a second order phase
transition driven by spin waves, together with a first order phase transition in the bond
variables between two bond ordered phases, one with local ferromagnetic order and another
with local antiferromagnetic order. We also prove that at the transition temperature the
bond-ordered phases coexist with a disordered phase as predicted by Domany, Schick and
Swendsen. This last result generalizes the result of Shlosman and van Enter
(cond-mat/0205455). We argue that these phenomena are quite general and should occur for a
large class of potentials