King's College London

Research portal

Manifolds in a high-dimensional random landscape: Complexity of stationary points and depinning

Research output: Contribution to journalArticlepeer-review

Standard

Manifolds in a high-dimensional random landscape : Complexity of stationary points and depinning. / Fyodorov, Yan V.; Le Doussal, Pierre.

In: PHYSICAL REVIEW E, Vol. 101, No. 2, 020101(R), 18.02.2020.

Research output: Contribution to journalArticlepeer-review

Harvard

Fyodorov, YV & Le Doussal, P 2020, 'Manifolds in a high-dimensional random landscape: Complexity of stationary points and depinning', PHYSICAL REVIEW E, vol. 101, no. 2, 020101(R). https://doi.org/10.1103/PhysRevE.101.020101

APA

Fyodorov, Y. V., & Le Doussal, P. (2020). Manifolds in a high-dimensional random landscape: Complexity of stationary points and depinning. PHYSICAL REVIEW E, 101(2), [020101(R)]. https://doi.org/10.1103/PhysRevE.101.020101

Vancouver

Fyodorov YV, Le Doussal P. Manifolds in a high-dimensional random landscape: Complexity of stationary points and depinning. PHYSICAL REVIEW E. 2020 Feb 18;101(2). 020101(R). https://doi.org/10.1103/PhysRevE.101.020101

Author

Fyodorov, Yan V. ; Le Doussal, Pierre. / Manifolds in a high-dimensional random landscape : Complexity of stationary points and depinning. In: PHYSICAL REVIEW E. 2020 ; Vol. 101, No. 2.

Bibtex Download

@article{0eb5733d0713464494673b37e8da8512,
title = "Manifolds in a high-dimensional random landscape: Complexity of stationary points and depinning",
abstract = "We obtain explicit expressions for the annealed complexities associated, respectively, with the total number of (i) stationary points and (ii) local minima of the energy landscape for an elastic manifold with internal dimension d<4 embedded in a random medium of dimension N≫1 and confined by a parabolic potential with the curvature parameter μ. These complexities are found to both vanish at the critical value μc identified as the Larkin mass. For μ<μc the system is in complex phase corresponding to the replica symmetry breaking in its T=0 thermodynamics. The complexities vanish, respectively, quadratically (stationary points) and cubically (minima) at μc-. For d≥1 they admit a finite {"}massless{"} limit μ=0 which is used to provide an upper bound for the depinning threshold under an applied force.",
author = "Fyodorov, {Yan V.} and {Le Doussal}, Pierre",
year = "2020",
month = feb,
day = "18",
doi = "10.1103/PhysRevE.101.020101",
language = "English",
volume = "101",
journal = "PHYSICAL REVIEW E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "2",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - Manifolds in a high-dimensional random landscape

T2 - Complexity of stationary points and depinning

AU - Fyodorov, Yan V.

AU - Le Doussal, Pierre

PY - 2020/2/18

Y1 - 2020/2/18

N2 - We obtain explicit expressions for the annealed complexities associated, respectively, with the total number of (i) stationary points and (ii) local minima of the energy landscape for an elastic manifold with internal dimension d<4 embedded in a random medium of dimension N≫1 and confined by a parabolic potential with the curvature parameter μ. These complexities are found to both vanish at the critical value μc identified as the Larkin mass. For μ<μc the system is in complex phase corresponding to the replica symmetry breaking in its T=0 thermodynamics. The complexities vanish, respectively, quadratically (stationary points) and cubically (minima) at μc-. For d≥1 they admit a finite "massless" limit μ=0 which is used to provide an upper bound for the depinning threshold under an applied force.

AB - We obtain explicit expressions for the annealed complexities associated, respectively, with the total number of (i) stationary points and (ii) local minima of the energy landscape for an elastic manifold with internal dimension d<4 embedded in a random medium of dimension N≫1 and confined by a parabolic potential with the curvature parameter μ. These complexities are found to both vanish at the critical value μc identified as the Larkin mass. For μ<μc the system is in complex phase corresponding to the replica symmetry breaking in its T=0 thermodynamics. The complexities vanish, respectively, quadratically (stationary points) and cubically (minima) at μc-. For d≥1 they admit a finite "massless" limit μ=0 which is used to provide an upper bound for the depinning threshold under an applied force.

UR - http://www.scopus.com/inward/record.url?scp=85080103276&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.101.020101

DO - 10.1103/PhysRevE.101.020101

M3 - Article

AN - SCOPUS:85080103276

VL - 101

JO - PHYSICAL REVIEW E

JF - PHYSICAL REVIEW E

SN - 1539-3755

IS - 2

M1 - 020101(R)

ER -

View graph of relations

© 2020 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454