  We explore the critical behaviour of two and three dimensional lattice models
of polymers in dilute solution where the monomers carry a magnetic moment which
interacts ferromagnetically with near-neighbour monomers. Specifically, the
model explored consists of a self-avoiding walk on a square or cubic lattice
with Ising spins on the visited sites. In three dimensions we confirm and
extend previous numerical work, showing clearly the first-order character of
both the magnetic transition and polymer collapse, which happen together. We
present results for the first time in two dimensions, where the transition is
seen to be continuous. Finite-size scaling is used to extract estimates for the
critical exponents and transition temperature in the absence of an external
magnetic field.
