IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v630y2023ics0378437123008014.html
   My bibliography  Save this article

The role of multiplicative noise in critical dynamics

Author

Listed:
  • Silvano, Nathan O.
  • Barci, Daniel G.

Abstract

We study the role of multiplicative stochastic processes in the description of the dynamics of an order parameter near a critical point. We study equilibrium as well as out-of-equilibrium properties. By means of a functional formalism, we build the Dynamical Renormalization Group equations for a real scalar order parameter with Z2 symmetry, driven by a class of multiplicative stochastic processes with the same symmetry. We compute the flux diagram using a controlled ϵ-expansion, up to order ϵ2. We find that, for dimensions d=4−ϵ, the additive dynamic fixed point is unstable. The flux runs to a multiplicative fixed point driven by a diffusion function G(ϕ)=1+g∗ϕ2(x)/2, where ϕ is the order parameter and g∗=ϵ2/18 is the fixed point value of the multiplicative noise coupling constant. We show that, even though the position of the fixed point depends on the stochastic prescription, the critical exponents do not. Therefore, different dynamics driven by different stochastic prescriptions (such as Itô, Stratonovich, anti-Itô and so on) are in the same universality class.

Suggested Citation

  • Silvano, Nathan O. & Barci, Daniel G., 2023. "The role of multiplicative noise in critical dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    • Handle: RePEc:eee:phsmap:v:630:y:2023:i:c:s0378437123008014
    DOI: 10.1016/j.physa.2023.129246
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123008014
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2023.129246?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lançon, P. & Batrouni, G. & Lobry, L. & Ostrowsky, N., 2002. "Brownian walker in a confined geometry leading to a space-dependent diffusion coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 304(1), pages 65-76.
    2. Arenas, Zochil González & Barci, Daniel G. & Moreno, Miguel Vera, 2018. "Stochastic dynamics of planar magnetic moments in a three-dimensional environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 98-109.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bringuier, E., 2012. "Transport of volume in a binary liquid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5064-5075.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:630:y:2023:i:c:s0378437123008014. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.