SciPost Physics

SciPost Phys. 10, 002 (2021) · published 4 January 2021

• doi: 10.21468/SciPostPhys.10.1.002
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical $p$-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

• Folena et al., Equilibrium fluctuations in mean-field disordered models
  Phys. Rev. E 106, 024605 (2022) [Crossref]
• Franz et al., Linear low energy excitations in fully-connected models of glasses
  J. Stat. Mech. 2022, 053302 (2022) [Crossref]
• Pacco et al., Overlaps between eigenvectors of spiked, correlated random matrices: From matrix principal component analysis to random Gaussian landscapes
  Phys. Rev. E 108, 024145 (2023) [Crossref]
• Ghimenti et al., Accelerating, to some extent, the p -spin dynamics
  Phys. Rev. E 105, 054137 (2022) [Crossref]
• Barbier et al., Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington–Kirkpatrick model
  J. Stat. Mech. 2021, 073301 (2021) [Crossref]
• Rizzo, Path integral approach unveils role of complex energy landscape for activated dynamics of glassy systems
  Phys. Rev. B 104, 094203 (2021) [Crossref]
• Carbone et al., Competition between energy- and entropy-driven activation in glasses
  Phys. Rev. E 106, 024603 (2022) [Crossref]
• Pacco et al., Curvature-driven pathways interpolating between stationary points: the case of the pure spherical 3-spin model
  J. Phys. A: Math. Theor. 57, 07LT01 (2024) [Crossref]
• Kent-Dobias et al., Analytic continuation over complex landscapes
  J. Phys. A: Math. Theor. 55, 434006 (2022) [Crossref]
• Mauri et al., Transition paths in Potts-like energy landscapes: General properties and application to protein sequence models
  Phys. Rev. E 108, 024141 (2023) [Crossref]
• Kent-Dobias et al., How to count in hierarchical landscapes: A full solution to mean-field complexity
  Phys. Rev. E 107, 064111 (2023) [Crossref]
• Correale et al., Probing chaos in the spherical p-spin glass model
  SciPost Phys. 15, 190 (2023) [Crossref]
• da Silva et al.,
  2, 177 (2024) [Crossref]
• Charbonneau et al., Jamming, relaxation, and memory in a minimally structured glass former
  Phys. Rev. E 108, 054102 (2023) [Crossref]