Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization

Abstract : We consider the long-ranged Ising spin-glass with random couplings decaying as a power-law of the distance, in the region of parameters where the spin-glass phase exists with a positive droplet exponent. For the Metropolis single-spin-flip dynamics near zero temperature, we construct via real-space renormalization the full hierarchy of relaxation times of the master equation for any given realization of the random couplings. We then analyze the probability distribution of dynamical barriers as a function of the spatial scale. This real-space renormalization procedure represents a simple explicit example of the droplet scaling theory, where the convergence towards local equilibrium on larger and larger scales is governed by a strong hierarchy of activated dynamical processes, with valleys within valleys.
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Submitted on : Thursday, July 31, 2014 - 10:39:23 AM
Last modification on : Thursday, July 18, 2019 - 10:30:05 AM

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Cécile Monthus. Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2014, 14, pp.P08009. ⟨10.1088/1742-5468/2014/08/P08009⟩. ⟨cea-01053482⟩

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