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

The coil-globule transition of an isolated polymer has been well establishe d to be a second-order phase transition described by a standard tricritical O(0) held theory. We provide compelling evidence from Monte Carlo simulati ons in four dimensions, where mean-field theory should apply, that the appr oach to this (tri)critical point is dominated by the build-up of first-orde r-like singularities masking the second-order nature of the coil-globule tr ansition: the distribution of the internal energy having two clear peaks th at become more distinct and sharp as the tricritical point is approached. H owever, the distance between the peaks slowly decays to zero. The evidence shows that the position of this (pseudo) first-order transition is shifted by an amount from the tricritical point that is asymptotically much larger than the width of the transition region.