Stretched exponential relaxation in systems with random free energies

Dominicis, C. De; Orland, Henri; Lainée, F.

doi:10.1051/jphyslet:019850046011046300

Cited by 111 publications

(77 citation statements)

References 12 publications

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“…This suggests that in the case of limestone samples, the close-to-uniform distribution of pore sizes occurs, whereas, in the case of Węglowicki sandstone, the pore distribution is well approximated by the self-scaling distribution [14].…”

Section: Table IVmentioning

confidence: 98%

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Liquid Phase Contained in Porous Rock as Observed by Proton Magnetic Relaxation

Harańczyk

Wójcik

2000

Acta Phys. Pol. A

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High power proton relaxometry was applied to investigate the liquid phase contained in porous rock. Proton free induction decays and spin-lattice relaxation times allowed us to investigate the pore distribution and the contribution of mobile and of immobilized liquid. The differences in pore distributions in oil-containing limestone and in Węglowicki sandstone were found. The fractal exponent for pore distribution in Węglowicki sandstone was fitted using both stretched exponential and modified stretched exponential models. The results of both approaches are compared.

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Section: Table IVmentioning

confidence: 98%

“…To test this hypothesis we fitted the stretched exponential (SE) function. Such function describes the fractal distribution of pores [14] The stretched exponential fits are shown in Table IIIb. Either the values of T1 , T2 or the amplitude values are close to the ones fitted using the single exponential fits.…”

Section: Table IIImentioning

confidence: 99%

Liquid Phase Contained in Porous Rock as Observed by Proton Magnetic Relaxation

Harańczyk

Wójcik

2000

Acta Phys. Pol. A

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“…21,22 The constant c is the infinite-time limit of M(T ). We have taken t from 10 4 to 10 6 MC steps per spin in the simulation.…”

Section: Skyrmion Crystal At Finite Temperaturesmentioning

confidence: 99%

“…[20][21][22] The relaxation time increases rapidly when T tends to T c . This increase is a consequence of the so-called "critical slowing-down".…”

Section: Skyrmion Crystal At Finite Temperaturesmentioning

confidence: 99%

Skyrmion crystals: Dynamics and phase transition

2017

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We study a crystal of skyrmions generated on a square lattice using a ferromagnetic exchange interaction and a Dzyaloshinskii-Moriya interaction between nearest-neighbors under an external magnetic field. The skyrmion crystal has a hexagonal structure which is shown to be stable up to a temperature Tc where a transition to the paramagnetic phase occur. We will show that the dynamics of the skyrmions at T < Tc follows a stretched exponential law.

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“…e −βE P (C ) , which we shall also write in the form P eq (C ) = Z −1 e −βE(C ) where E(C ) comprises an energy component and an entropy component, and where n 0 is the average occupation number and β is the inverse temperature. It is known since the work of De Dominicis et al [29] that picking transition rates between configurations C and C such that W (C → C ) = P eq (C ) leads to a master equation whose spectrum is made of the zero eigenvalue of the equilibrium state, and a unit eigenvalue (with of course a very large degeneracy). Under such conditions, the dynamics, and thus all time correlations, will exponentially relax to equilibrium at unit rate.…”

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confidence: 99%

Brownian dynamics: From glassy to trivial

et al. 2015

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We endow a system of interacting particles with two distinct, local, Markovian and reversible microscopic dynamics. Using common field-theoretic techniques used to investigate the presence of a glass transition, we find that while the first, standard, dynamical rules lead to glassy behavior, the other one leads to a simple exponential relaxation towards equilibrium. This finding questions the intrinsic link that exists between the underlying, thermodynamical, energy landscape, and the dynamical rules with which this landscape is explored by the system. Our peculiar choice of dynamical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.The microscopic phenomena driving the dynamical arrest in supercooled liquids and in glasses are still controversial. One line of thought, which originates in the work of Adam and Gibbs, pictures a glass-forming liquid as a system whose energy landscape complexity accounts for the slowing down of its dynamics. The original Adam-Gibbs [1] theory relates viscosity -the momentum transport coefficient-to configurational entropy. The more recent scenario due to Kirkpatrick, Thirumalai, and Wolynes [2] is based on the study of the metastable configurations of the system and on the concept of nucleating entropic droplets. This is the Random-First-Order Theory (RFOT) scenario. The idea is that metastability arises from the many valleys of the energy landscape the system can be trapped in. The RFOT scenario gives a large set of quantitative predictions including non-mean field particle models [4]. These aspects of the physics of glasses were reviewed by Debenedetti and Stillinger [5] and more recently by Biroli and Bouchaud [6].In another line of thought, no complex energy landscape needs to be invoked, and dynamically induced metastability alone is held responsible for the dynamics slowing down. This is a phenomenological approach in which at a coarse-grained scale local patches of activity are the only ingredients of the dynamics. This has led to the development of kinetically-constrained models (KCM) (see [7] for a review), which have the advantage of lending themselves with greater ease than molecular models to both numerical experiments and analytical treatment. The hallmark of the corresponding lattice models is the absence of any structure in the energy landscape (the equilibrium distribution is that of independent degrees of freedom). These somewhat simplistic descriptions are not directly built from the microscopics, and it is often argued that their glassy-like properties, like the existence of dynamical heterogeneities, are almost tautological, but recent works [8] have tried to bridge the gap from the microscopics to dynamic facilitation.A central concept in both approaches is that of metastability. A metastable state can be viewed as an eigenstate of the evolution operator with a nonzero but small relaxation rate. The existe...

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Stretched exponential relaxation in systems with random free energies

Cited by 111 publications

References 12 publications

Liquid Phase Contained in Porous Rock as Observed by Proton Magnetic Relaxation

Liquid Phase Contained in Porous Rock as Observed by Proton Magnetic Relaxation

Skyrmion crystals: Dynamics and phase transition

Brownian dynamics: From glassy to trivial

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