Extended droplet theory for aging in short-range spin glasses and a numerical examination

Yoshino, Hajime; Hukushima, Koji; Takayama, Hajime

doi:10.1103/physrevb.66.064431

Cited by 41 publications

(77 citation statements)

References 67 publications

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“…In fact, the growth of the dynamical correlation length at the critical point of different three-and fourdimensional spin glasses has been intensively investigated in the recent past. We mention here the Ising spin glass with a Bimodal 29,30 or a Gaussian 21,30 distribution of the couplings, the gauge glass with a Gaussian distribution 21 , the XY spin glass with a Bimodal distribution 31 Heisenberg spin glass with a Gaussian distribution 32 . All these studies reveal that for times t ≥ 20 the increase of the dynamical correlation length in various spin glasses (including some of the cases we consider in this work) is given by the simple power-law (26).…”

Section: Dimensionmentioning

confidence: 99%

Dynamic critical behavior in Ising spin glasses

Pleimling

Campbell

2005

Phys. Rev. B

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The critical dynamics of Ising spin glasses with Bimodal, Gaussian, and Laplacian interaction distributions are studied numerically in dimensions 3 and 4. The data demonstrate that in both dimensions the critical dynamic exponent zc, the non-equilibrium autocorrelation decay exponent λc/zc, and the critical fluctuation-dissipation ratio X∞ all vary strongly and systematically with the form of the interaction distribution.

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Section: Dimensionmentioning

confidence: 99%

Dynamic critical behavior in Ising spin glasses

Pleimling

Campbell

2005

Phys. Rev. B

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“…This conjecture was supported both by numerical simulation [3] and analytic work [4] (see, however, also ref. [5]). …”

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confidence: 99%

Fluctuation-Dissipation Ratio of the Heisenberg Spin Glass

Kawamura

2003

Phys. Rev. Lett.

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Fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. Numerically determined FD ratio exhibits a "one-step-like" behavior, the effective temperature of the spin-glass state being about twice the spin-glass transition temperature, T eff ≃ 2Tg, irrespective of the bath temperature. The results are discussed in conjunction with the recent experiment by Hérisson and Ocio, and with the chirality scenario of spin-glass transition.Off-equilibrium dynamics of spin glass (SG) has attracted much recent interest [1]. In equilibrium, there holds a relation between the response and the correlation known as the fluctuation-dissipation theorem (FDT). In off-equilibrium, relaxation of physical quantities of SG depends on its previous history. Most typically, it depends not only on the observation time t but also on the waiting time t w , i.e., exhibits aging. While in the shorttime quasi-equilibrium regime t 0 << t << t w (t 0 is a microscopic time scale), relaxation is still stationary and FDT holds, it becomes non-stationary and FDT is broken in the long-time aging regime t >> t w . In particular, the breaking pattern of FDT, and its possible relation to the static quantity, has been the subject of recent active studies.A quantity playing a central role here is the so-called fluctuation-dissipation ratio (FDR) X, which may be defined by the relation,where R(t 1 , t 2 ) is a response function measured at time t 2 to an impulse field applied at time t 1 , C(t 1 , t 2 ) is a two-time correlation function in zero field at times t 1 and t 2 , and T is the bath temperature. One may regard T /X ≡ T eff as an effective temperature. In the case FDT holds, one has X = 1 and T eff = T . Via the study of certain mean-field models, Cugliandolo and Kurchan showed that, in the limit of infinite time t 1 , t 2 → ∞, the FDR X depended on the times t 1 and t 2 only through the correlation function C(t 1 , t 2 ), i.e., X(t 1 , t 2 ) = X(C(t 1 , t 2 )) [2]. It was further suggested that X(C) could be related to an appropriate static quantity, i.e., X(C) is equivalent to the x(q)-function describing the replica-symmetry breaking (RSB) pattern in the Parisi's scheme, which is related to the overlap distribution function via P (q) = dx(q) dq [2]. This conjecture was supported both by numerical simulation [3] and analytic work [4] (see, however, also ref. [5]).Experimental studies on the FDR of SG have been hampered for a long time by the difficulty in performing high-precision measurements of correlations (noise measurements), although some interesting preliminary results were reported [6]. Recently, however, a remarkable experiment by Hérisson and Ocio for an insulating Heisenberg SG CdCr 1.7 In 0.3 S 4 has eventually opened a door to experimental access to the FDR of SG [7]. Some comparison was already made between these expeirmental results and the numerical results obtained by offequilibrium simulation on certain SG models.Meanwhile,...

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“…In [17] it is shown that quantum fluctuations in quantum glassy systems depress the phase transition temperature, in a glassy phase the aging effect survives the quantum fluctuations, and because of quantum fluctuations, the fluctuation-dissipation theorem is modified. In reference [19][20][21] it is shown that all terms in the dynamical equations governing the timeevolution of spin response and correlation function which are due to quantum effects, are irrelevant at long times. Quantum effects enter only through the renormalization of parameters in dynamical equations [19][20][21].…”

Section:  mentioning

confidence: 99%

“…is described by this model hamiltonian [4,13,20]. It is supposed that this model may also represent, for example, the physics of deuteron glass such as…”

Section: Model Hamiltonianmentioning

confidence: 99%

“…The natural basis for the interpretation of aging is based on coarsening ideas of a slow domain growth of a spin-glass type ordered phase [8,13,14]. A large attention in the last decade was paid to the spin glasses representing a model systems for study of non-equilibrium dynamics providing a measure of processes causing the aging: the magnetic susceptibility [15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Out-of-Equilibrium Dissipative <i>ac</i>—Susceptibility in Quantum Ising Spin Glass

Busiello¹

2013

JMP

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The imaginary part of the non-equilibrium magnetic susceptibility of Ising spin glass in a transverse field under timedependent longitudinal external magnetic field has been calculated at very low temperature on the basis of quantum droplet model and quantum linear response theory. Quantum and aging effects on the low temperature dynamics of the model are discussed. A comparison with recent theoretical and experimental data in spin glass is made.

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Extended droplet theory for aging in short-range spin glasses and a numerical examination

Cited by 41 publications

References 67 publications

Dynamic critical behavior in Ising spin glasses

Dynamic critical behavior in Ising spin glasses

Fluctuation-Dissipation Ratio of the Heisenberg Spin Glass

Out-of-Equilibrium Dissipative <i>ac</i>—Susceptibility in Quantum Ising Spin Glass

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Extended droplet theory for aging in short-range spin glasses and a numerical examination

Cited by 41 publications

References 67 publications

Dynamic critical behavior in Ising spin glasses

Dynamic critical behavior in Ising spin glasses

Fluctuation-Dissipation Ratio of the Heisenberg Spin Glass

Out-of-Equilibrium Dissipative &lt;i&gt;ac&lt;/i&gt;—Susceptibility in Quantum Ising Spin Glass

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Out-of-Equilibrium Dissipative <i>ac</i>—Susceptibility in Quantum Ising Spin Glass