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The coil-globule transition of an isolated polymer has been well establishedto be a second-order phase transition described by a standard tricritical O(0)field theory. We provide compelling evidence from Monte Carlo simulations infour dimensions, where mean-field theory should apply, that the approach tothis (tri)critical point is dominated by the build-up of first-order-likesingularities masking the second-order nature of the coil-globule transition:the distribution of the internal energy having two clear peaks that become moredistinct and sharp as the tricritical point is approached. However, thedistance between the peaks slowly decays to zero. The evidence shows that theposition of this (pseudo) first-order transition is shifted by an amount fromthe tricritical point that is asymptotically much larger than the width of thetransition region. We suggest an explanation for the apparently contradictoryscaling predictions in the literature.Comment: 4 pages, 2 figures included in tex

First-order scaling near a second-order phase transition: Tricritical polymer collapse