  The coil-globule transition of an isolated polymer has been well established
to be a second-order phase transition described by a standard tricritical O(0)
field theory. We present Monte-Carlo simulations of interacting self-avoiding
walks and interacting self-avoiding trails in four dimensions which provide
compelling evidence that the approach to this (tri)critical point is dominated
by the build-up of first-order-like singularities masking the second-order
nature of the coil-globule transition.
