Order of phase transitions in barrier crossing

J. Bürki, C. A. Stafford, and D. L. Stein
Phys. Rev. E 77, 061115 – Published 11 June 2008

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.

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  • Received 12 February 2008

DOI:https://doi.org/10.1103/PhysRevE.77.061115

©2008 American Physical Society

Authors & Affiliations

J. Bürki and C. A. Stafford

  • Physics Department, University of Arizona, 1118 East 4th Street, Tucson, Arizona 85721, USA

D. L. Stein

  • Department of Physics and Courant Institute of Mathematical Sciences, New York University, New York, New York 10003, USA

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Issue

Vol. 77, Iss. 6 — June 2008

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