Related Experiment Video
Updated: Jul 3, 2026

Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers
Published on: September 4, 2015
Order of phase transitions in barrier crossing
J Bürki1, C A Stafford, D L Stein
1Physics Department, University of Arizona, Tucson, Arizona 85721, USA.
Abstract:
A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the transition can be first or second order, but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier. In this paper, we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary in both space and time, and whose zero-noise dynamics are governed by a smooth polynomial potential. We show that a quartic potential barrier can have only second-order transitions, confirming an earlier conjecture [D. L. Stein, J. Stat. Phys. 114, 1537 (2004)]. We then derive, through a combination of analytical and numerical arguments, both necessary and sufficient conditions to have a first-order vs a second-order transition in noise-induced activation behavior, for a large class of systems with smooth polynomial potentials of arbitrary order. We find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier.
More Related Videos
06:26Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
Published on: May 15, 2017
10:08Phase Behavior of Charged Vesicles Under Symmetric and Asymmetric Solution Conditions Monitored with Fluorescence Microscopy
Published on: October 24, 2017
Related Concept Videos
Phase Transitions
Phase Transitions
Phase Diagram
Phase Diagram
Phase Transitions: Sublimation and Deposition
Phase Transitions: Melting and Freezing