Spin-glass dynamics and the barrier model: Extraction of the Parisi physical order parameter
Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
Cited by 6 publications
References 22 publications
The mesoscale allows a new probe of spin glass dynamics. Because of the spin glasses lower critical dimension d l > 2, the growth of the correlation length ξ(t, T ) can change the nature of the spin glass state at a crossover time tco when ξ(tco, T ) = ℓ, a minimum characteristic sample length (i.e. film thickness for thin films and crystallite size for bulk samples). For thin films, and times t < tco such that ξ(t, T ) < ℓ, conventional three dimensional dynamics are observed. When t > tco, a crossover to d = 2 behavior takes place. The parallel correlation length, associated with a Tg = 0 transition, increases in time from the saturated value of the perpendicular correlation length ℓ to an equilibrium value of the parallel correlation length proportional to T −ν . This results in a pancake-like correlated state, with a thickness ℓ and a temperature dependent in-plane radius that increases with decreasing temperature. Activated dynamics are associated with these states. Measurements on Cu:Mn thin films are analyzed quantitatively within this framework. We extract a temperature dependent activation energy from a fit to the frequency dependence of the dynamic susceptibility. The extrapolated temperature at which the activation energy would become large is close to the extrapolated glass transition temperature from ac susceptibility measurements. All known relevant experimental data are consistent with this approach. For polycrystalline materials, there is a distribution of length scales P(ℓ). For sufficiently broad distributions, a logarithmic time dependence is derived for the time decay of the thermoremanent magnetization MTRM(t, T ) using an approach originally derived by Ma. Properties dependent upon an effective waiting time t eff w are derived that are consistent with experiment, and further measurements are suggested.
The mesoscale allows a new probe of spin glass dynamics. Because of the spin glasses lower critical dimension d l > 2, the growth of the correlation length ξ(t, T ) can change the nature of the spin glass state at a crossover time tco when ξ(tco, T ) = ℓ, a minimum characteristic sample length (i.e. film thickness for thin films and crystallite size for bulk samples). For thin films, and times t < tco such that ξ(t, T ) < ℓ, conventional three dimensional dynamics are observed. When t > tco, a crossover to d = 2 behavior takes place. The parallel correlation length, associated with a Tg = 0 transition, increases in time from the saturated value of the perpendicular correlation length ℓ to an equilibrium value of the parallel correlation length proportional to T −ν . This results in a pancake-like correlated state, with a thickness ℓ and a temperature dependent in-plane radius that increases with decreasing temperature. Activated dynamics are associated with these states. Measurements on Cu:Mn thin films are analyzed quantitatively within this framework. We extract a temperature dependent activation energy from a fit to the frequency dependence of the dynamic susceptibility. The extrapolated temperature at which the activation energy would become large is close to the extrapolated glass transition temperature from ac susceptibility measurements. All known relevant experimental data are consistent with this approach. For polycrystalline materials, there is a distribution of length scales P(ℓ). For sufficiently broad distributions, a logarithmic time dependence is derived for the time decay of the thermoremanent magnetization MTRM(t, T ) using an approach originally derived by Ma. Properties dependent upon an effective waiting time t eff w are derived that are consistent with experiment, and further measurements are suggested.
We study analytically M -spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M . Our approach is primarily dynamical and is based on the convergence of σ t , a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit σ ∞ . The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations and relations to thermodynamic states. For example, we show that their overlap distribution is a deltafunction at zero. We also define a dynamics for M = ∞, which provides a potential tool for investigating ground state structure.
de Koning et al. Reply:
de Koning et al. Reply: In our Letter [1] we performed path-integral ground state (PIGS) calculations of dislocation cores in hcp 4 He to investigate the presence of offdiagonal long-range order (ODLRO) and assess the existence of a finite condensate fraction. We found that ODLRO is absent in all cases, with the systems displaying no significant difference from the insulating defect-free crystal. This result challenges the superfluid-dislocationnetwork interpretation for mass-flow observations in 4 He.Boninsegni et al.[2], hereafter referred to as BKPPS, contend that our criticism of their work is "unjustified". In particular, BKPPS argue that our disagreeing results are due to the adopted averaging procedure of the one-body density matrix and "an enhanced local pressure at the dislocation core". In the following, in addition to refuting BKPPS's contestations, we argue that the origin of the difference between our results and those reported by BKPPS is rooted in the application of appropriate boundary conditions for meaningful dislocation simulations.BKPPS question our approach with respect to the onebody density matrix (OBDM), ρ (r 1 , r 2 ). It is stated that we ignore its nonuniformity and anisotropy and that our averageing "leads to an enormous suppression of n 0 , . . .".First, the condensate fraction n 0 is a scalar quantity, defined for the system as a whole through the k → 0 limit of the momentum distribution, which, by definition, is isotropic. In fact, as has been shown in [3], even when ρ (r 1 , r 2 ) is anisotropic. it is only the isotropic component that persists at large separations. Second, the suggestion that a global cell average leads to an enormous suppression of the dislocation signal is incorrect. As demonstrated previously [4], PIGS simulations detected a significant condensate fraction (n 0 ∼ 10 −3 ) for a monovacancy in a cell containing 180 atoms, in which the fraction of atoms neighboring the defected region is ∼ 10 −2 . In our simulations this fraction is of the same order of magnitude. Moreover, it is crucial to point out that, at the atomic level, a dislocation core is not a 1-dimensional object (BKPPS refer to one-dimensional superfluidity). Instead, it constitutes a truly 3-dimensional tube-like region with a cross-section determined by the core radius, which may span several interatomic spacings. Accordingly, the volume occupied by the defected region represents a non-negligible fraction of the simulation cell and if the dislocation core had contributed to a finite condensate fraction, it would have been detected.Subsequently, BKPPS raise the issue of the finite size of the cells and argue that our cells would be "at elevated bulk pressure" compared to the bulk crystal, such that the OBDM for the CS and CE dislocations "are suppressed in comparison with the one for the ideal crystal".These arguments are moot, given that all our results were obtained at the same number density of 0.0287 Å−3 for which the superfluidity claims were reported in Refs. [5,6]. Furthermore, the finite-size...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
Contact Info
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Product
Resources
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2025 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.
