Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                

Dimensional crossover in the aging dynamics of spin glasses in a film geometry

L. A. Fernandez, E. Marinari, V. Martin-Mayor, I. Paga, and J. J. Ruiz-Lorenzo
Phys. Rev. B 100, 184412 – Published 11 November 2019
PDFHTMLExport Citation
Abstract
Authors
Article Text
  • INTRODUCTION
  • 2D AND 3D SPIN-GLASS DYNAMICS
  • MODEL AND PROTOCOL
  • RESULTS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Motivated by recent experiments of exceptional accuracy, we study numerically the spin-glass dynamics in a film geometry. We cover all the relevant time regimes, from picoseconds to equilibrium, at temperatures at and below the 3D critical point. The dimensional crossover from 3D to 2D dynamics, which starts when the correlation length becomes comparable to the film thickness, consists of four dynamical regimes. Our analysis, based on a renormalization group transformation, finds consistent the overall physical picture employed by Orbach and co-workers in the interpretation of their experiments.

    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    1 More
    • Received 4 June 2019
    • Revised 23 October 2019

    DOI:https://doi.org/10.1103/PhysRevB.100.184412

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Statistical field theory
    1. Physical Systems
    Nonequilibrium systemsSpin glasses
    1. Techniques
    Finite-size scalingStatistical methods
    Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

    Authors & Affiliations

    L. A. Fernandez1,2, E. Marinari3, V. Martin-Mayor1,2, I. Paga4,1, and J. J. Ruiz-Lorenzo5,6,2

    • 1Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain
    • 2Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
    • 3Dipartimento di Fisica, Sapienza Università di Roma, INFN, Sezione di Roma 1, and CNR-Nanotec, I-00185 Rome, Italy
    • 4Dipartimento di Fisica, Sapienza Università di Roma, INFN, Sezione di Roma 1, Italy
    • 5Departamento de Física, Universidad de Extremadura, 06006 Badajoz, Spain
    • 6Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 100, Iss. 18 — 1 November 2019

    Reuse & Permissions
    Access Options
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required

    Log In
    Other Options
    ×

    Images

    • Figure 1
      Figure 1

      The longitudinal correlation length ξ12∥(T,t), as computed in films of thickness Lz, versus the waiting time t after a quench to temperature T, for T=0.98 (main), T=1.1 (upper inset), and T=0.7 (lower inset). The critical temperature is Tc=1.102(3) [38]. As a reference, we also show purely 3D dynamics (data taken from Ref. [15]) and fits to 2D dynamics ξ12∥(Lz,T,t)≈b(Lz,T)+a(Lz,T)t1/z2D, with z2D=7.14 [16] [fit parameters: b(Lz,T) and a(Lz,T)].

      Reuse & Permissions
    • Figure 2
      Figure 2

      Growth of the longitudinal ξ12∥ (solid lines) and of the transversal ξ12⊥ (dashes lines) correlation lengths with the waiting time t after a quench to temperature T. The inset (for Lz=8) is a zoom of the saturation of ξ12⊥ and of the separation between the ξ12∥ and the bulk correlation length (see the main text for more details).

      Reuse & Permissions
    • Figure 3
      Figure 3

      Dynamical scale invariance for the dimensionless quantity ξ12film(t)/ξ123D(t) as a function of the rescaled bulk length ξ123D(t)/Lz.

      Reuse & Permissions
    • Figure 4
      Figure 4

      The scale-invariant ratio ξ23RG(T,t)/ξ12RG(T,t), versus the ratio ξ12RG(t,T)/ξ12RG,eq(T) as computed from the block spins [ξ12RG(t,T) grows monotonically to its equilibrium value ξ12RG,eq(T)]. For T=1.1≈Tc and T=0.98≈0.9Tc, we compare the scaling function obtained from block spins (as extracted from films of several thicknesses Lz), with two analogous functions computed in purely 2D systems. If the 2D system is considered at the film's temperature T2D=T, the scaling function ξ232D(T,t)/ξ122D(T,t) clearly differs from the block-spin result. On the other hand, the film and the 2D scaling function essentially coincide if the 2D system is considered at the effective temperature Teff,2D defined by Eq. (4).

      Reuse & Permissions
    • Figure 5
      Figure 5

      Squared statistical error for ξ12(Tc,t=222,Lz=4), as computed from a set of NS=128 samples and NR replicas, versus NR. The dashed line is a fit to Eq. (B1). The relevant quantities extracted from the fit are σR2/σS2≈156 and x≈0.65. For reference, we show with continuous lines the two extremal behaviors, namely x=1 (with Δ∝1/NR2) and x=0.5 (with Δ∝1/NR). Because σR2≫σS2, Δ shows an intermediate behavior for small NR. However, when NR>30 the contribution of thermal fluctuations to the final error becomes comparable to the sample contribution and there is little gain in further increasing NR.

      Reuse & Permissions
    • Figure 6
      Figure 6

      Growth of the transversal correlation length ξ12⊥(T,t) at T=0.98 as a function of the waiting time t in log-log scale. The PBC (OBC) case is depicted in solid (dashed) lines.

      Reuse & Permissions
    • Figure 7
      Figure 7

      Growth of the longitudinal correlation length ξ12∥(T,t) at T=0.98 as a function of the waiting time t as computed with periodic boundary conditions (PBCs) or with open boundary conditions (OBCs) on the central layer (ZMED) or on the top layer (ZTOP). The inset shows the data from the main panel in the full time range of our simulations.

      Reuse & Permissions
    • Figure 8
      Figure 8

      Dynamical scale invariance for the dimensionless quantity ξ12∥(t)/ξ123D(t) as a function of the rescaled bulk length ξ123D(t)/Lz, for the PBC case (solid), for the OBC central layer (dashed), and for the OBC external layer (dotted) at temperatures T=0.98 (top) and T=1.1 (bottom).

      Reuse & Permissions
    ×

    Sign up to receive regular email alerts from Physical Review B

    Log In

    Cancel
    ×

    Search

    Article Lookup

    Paste a citation or DOI
    Enter a citation
    ×