Order of phase transitions in barrier crossing

J. Bürki, C. A. Stafford, D. L. Stein

    Research output: Contribution to journalArticle

    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
    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

    Bürki, J., Stafford, C. A., & Stein, D. L. (2008). Order of phase transitions in barrier crossing. Physical Review E, 77(6), [061115]. https://doi.org/10.1103/PhysRevE.77.061115

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

    In: Physical Review E, Vol. 77, No. 6, 061115, 11.06.2008.

    Research output: Contribution to journalArticle

    Bürki, J, Stafford, CA & Stein, DL 2008, 'Order of phase transitions in barrier crossing', Physical Review E, vol. 77, no. 6, 061115. https://doi.org/10.1103/PhysRevE.77.061115
    Bürki, J. ; Stafford, C. A. ; Stein, D. L. / Order of phase transitions in barrier crossing. In: Physical Review E. 2008 ; Vol. 77, No. 6.
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