Order of phase transitions in barrier crossing

J. Bürki, Charles A Stafford, D. L. Stein

Research output: Contribution to journalArticle

4 Citations (Scopus)

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. 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.

Original languageEnglish (US)
Article number061115
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume77
Issue number6
DOIs
StatePublished - Jun 11 2008

Fingerprint

Phase Transition
Activation
polynomials
activation
First-order
Polynomial
Metastable States
Quartic
metastable state
Order Parameter
Vary
Necessary Conditions
Sufficient Conditions
Zero
Arbitrary
Class

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Order of phase transitions in barrier crossing. / Bürki, J.; Stafford, Charles A; Stein, D. L.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 77, No. 6, 061115, 11.06.2008.

Research output: Contribution to journalArticle

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