Research output: Contribution to journal › Article › peer-review

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

Research output: Contribution to journal › Article › peer-review

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

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

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

@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",

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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.

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U2 - 10.1103/PhysRevE.101.020101

DO - 10.1103/PhysRevE.101.020101

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VL - 101

JO - PHYSICAL REVIEW E

JF - PHYSICAL REVIEW E

SN - 1539-3755

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M1 - 020101(R)

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