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

TL;DR

This paper investigates the approach to a tricritical point in polymer collapse, revealing first-order-like singularities that mask the second-order transition, supported by Monte Carlo simulations in four dimensions.

Contribution

It provides evidence that the coil-globule transition exhibits pseudo first-order behavior near the tricritical point, challenging previous scaling predictions.

Findings

Energy distribution shows two peaks becoming sharper near the tricritical point.

Peak separation decays slowly, indicating pseudo first-order transition behavior.

Shift of the transition point is larger than the transition width.

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. We suggest an explanation for the apparently contradictory scaling predictions in the literature.