Spreading of damage in the Sherrington—Kirkpatrick spherical spin glass

Stariolo, Daniel A.

doi:10.1080/13642819808204994

Cited by 1 publication

(1 citation statement)

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“…We conclude that for all temperatures, both p = 3 and p = 4, the asymptotic distance is independent of the initial distance. This is in contrast with the case p = 2, where dependence of the initial distance is found for the low temperature region 32 . We must say that we have obtained the same results, as in cases p = 3, 4, for a model which is a combination of the p = 2 and p = 4 spherical spin-glass model 40 .…”

Section: Numerical Analysiscontrasting

confidence: 85%

Damage spreading transition in glasses: A probe for the ruggedness of the configurational landscape

Heerema

Ritort

1999

Phys. Rev. E

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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 T 0 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 ͑i͒ independence of the initial damage; ͑ii͒ independence of the class of initial condition; and ͑iii͒ 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 states͒ 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 model͒ with Monte Carlo heatbath 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.

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Section: Numerical Analysiscontrasting

confidence: 85%