1998/12/31 by M. Heerema, M Heerema, F. Ritort +1 · 5 citations
Earth and Planetary Sciences · Materials Science · Mathematics · Physics and Astronomy · #Detailed balance #Energy landscape #Exponential function #Independence (probability theory) #Limit (mathematics) #Material Dynamics and Properties #Mathematical analysis #Mathematics #Mean field theory #Noise (video) #Physics #Quantum mechanics #Saddle #Saddle point #Statistical physics #Statistics #Theoretical and Computational Physics #Thermodynamic limit #Thermodynamics #Tree-ring climate responses #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.60.3646
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 60(4), 3646-3665 (American Physical Society) · 25 pages, 13 postscript figures. Paper extended to include cross-correlations
openalex publication_date 1999/10/01 · arxiv created 1999/11/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially large number of metastable states. For systems evolving under identical but arbitrarily correlated noises, we demonstrate that there exists a critical temperature T0 which separates two different dynamical regimes depending on whether damage spreads or not in the asymptotic long-time limit. This transition exists for generic noise correlations such that the zero damage solution is stable at high temperatures, being minimal for maximal noise correlations. Although this dynamical transition depends on the type of noise correlations, we show that the asymptotic damage has the good properties of a dynamical order parameter, such as (i) independence of the initial damage; (ii) independence of the class of initial condition; and (iii) stability of the transition in the presence of asymmetric interactions which violate detailed balance. For maximally correlated noises we suggest that damage spreading occurs due to the presence of a divergent number of saddle points (as well as metastable states) in the thermodynamic limit consequence of the ruggedness of the free-energy landscape which characterizes the glassy state. These results are then compared to extensive numerical simulations of a mean-field glass model (the Bernasconi model) with Monte Carlo heat-bath dynamics. The freedom of choosing arbitrary noise correlations for Langevin dynamics makes damage spreading an interesting tool to probe the ruggedness of the configurational landscape.