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

¹ Department of Mathematics and Statistics, The University of Melbourne 3010, Melbourne, Australia
² Department of Physics, Syracuse University Syracuse, NY 13244, USA

Corresponding authors: aleks@ms.unimelb.edu.au tprell@physics.syr.edu

Received: 8 February 2000
Accepted: 28 July 2000

Abstract

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 provide compelling evidence from Monte Carlo simulations in four dimensions, where mean-field theory should apply, 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: the distribution of the internal energy having two clear peaks that become more distinct and sharp as the tricritical point is approached. However, 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.