arXiv:cond-mat/0303116 · Physical review. B, Condensed matter

Real space renormalization group approach to spin-glass dynamics

F. Scheffler, Hajime Yoshino, Philipp Maass

Published Aug 19, 2003• 14 citations

Abstract

The slow nonequilibrium dynamics of the Edwards-Anderson spin-glass model on a hierarchical lattice is studied by means of a coarse-grained description based on renormalization concepts. We evaluate the isothermal aging properties and show how the occurrence of temperature chaos is connected to a gradual loss of memory when approaching the overlap length. This leads to rejuvenation effects in temperature shift protocols and to rejuvenation-memory effects in temperature cycling procedures with a pattern of behavior parallel to experimental observations.

DOI: 10.1103/physrevb.68.060404

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arXiv:cond-mat/0303116 · Physical review. B, Condensed matter

Real space renormalization group approach to spin-glass dynamics

F. Scheffler, Hajime Yoshino, Philipp Maass

Published Aug 19, 2003• 14 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.68.060404

Related papers

Rejuvenation and memory in model spin glasses in three and four dimensions

S. Jiménez, Víctor Martín-Mayor, Sergio Perez-Gaviro

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Physical Review BAug 15, 200526 citations

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達雄小森, Hajime Yoshino, Hajime Takayama

By means of Monte Carlo simulations on the three-dimensional Ising spin-glass model, we have studied aging phenomena with various temperature( $T$ )-change protocols. Particularly, a $T$ -shift protocol, in which a system is first quenched to and aged for a period $t_{\rm w1}$ at a temperature $T_1$ , and subsequently aged at a new temperature $T_2$ is closely investigated. Most importantly, the mean size of domains, which is extracted from the replica-overlap function, was found to grow monotonically without any appreciable decrease by the $T$ -change. We also found the relaxation of energy density and spin auto-correlation function during the $T$ -shift process can be explained within the following picture: the dynamics finally crossovers to an isothermal aging of $T_2$ at around $t_2 \simeq t_{\rm w1}^{\rm (eff)}$ after the $T$ -change, where $t_{\rm w1}^{\rm (eff)}$ is an effective waiting time related with $t_{\rm w1}$ , but in the transient regime $t_2 \lt t_{\rm w1}^{\rm (eff)}$ , adjustment of the population of thermally active droplets from that at $T_1$ to $T_2$ takes place very slowly. Implications of the results on aging phenomena in other $T$ -change protocols such as $T$ -cycling and continuous $T$ -change with an intermittent stop observed by simulations as well as experiments are discussed.By means of Monte Carlo simulations on the three-dimensional Ising spin-glass model, we have studied aging phenomena with various temperature($T$)-change protocols. Particularly, a $T$-shift protocol, in which a system is first quenched to and aged for a period $t_{\rm w1}$ at a temperature $T_1$, and subsequently aged at a new temperature $T_2$ is closely investigated. Most importantly, the mean size of domains, which is extracted from the replica-overlap function, was found to grow monotonically without any appreciable decrease by the $T$-change. We also found the relaxation of energy density and spin auto-correlation function during the $T$-shift process can be explained within the following picture: the dynamics finally crossovers to an isothermal aging of $T_2$ at around $t_2 \simeq t_{\rm w1}^{\rm (eff)}$ after the $T$-change, where $t_{\rm w1}^{\rm (eff)}$ is an effective waiting time related with $t_{\rm w1}$, but in the transient regime $t_2 \lt t_{\rm w1}^{\rm (eff)}$, adjustment of the population of thermally active droplets from that at $T_1$ to $T_2$ takes place very slowly. Implications of the results on aging phenomena in other $T$-change protocols such as $T$-cycling and continuous $T$-change with an intermittent stop observed by simulations as well as experiments are discussed.

arXiv:cond-mat/0001395Jan 27, 20007 citations

We numerically study aging for the Edwards-Anderson model in three and four dimensions using different temperature-change protocols. In

D=3

, time scales a thousand times larger than in previous work are reached with the Spin Update Engine (SUE) machine. Deviations from cumulative aging are observed in the nonmonotonic time behavior of the coherence length. Memory and rejuvenation effects are found in a temperature-cycle protocol, revealed by vanishing effective waiting times. Similar effects are reported for the

D=3

site-diluted ferromagnetic Ising model (without chaos). However, rejuvenation is reduced if off-equilibrium corrections to the fluctuation-dissipation theorem are considered. Memory and rejuvenation are quantitatively describable in terms of the growth regime of the spin-glass coherence length.

The temperature (

T

)-shift protcol of aging in the 3 dimensional (3D) Edwards- Anderson (EA) spin-glass (SG) model is studied through the out-of-phase component of the ac susceptibility simulated by the Monte Carlo method. For processes with a small magnitude of the

T

-shift,

ΔT

, the memory imprinted before the

T

-shift is preserved under the

T

-change and the SG short-range order continuously grows after the

T

-shift, which we call the cumulative memory scenario. For a negative

T

-shift process with a large

ΔT

the deviation from the cumulative memory scenario has been observed for the first time in the numerical simulation. We attribute the phenomenon to the `chaos effect' which, we argue, is qualitatively different from the so-called rejuvenation effect observed just after the

T

-shift.

{l}_{T}

such that length scales smaller than

{l}_{T}

are equilibrated, whereas larger length scales are essentially frozen. The time and temperature dependences of

{l}_{T}

are found to be compatible with critical power-law dynamical scaling for small times and high temperatures, crossing over to an activated logarithmic growth for longer times and lower temperatures, in agreement with recent experimental results. The activated regime is governed by a ``barrier exponent'' $\ensuremath{\psi}$ which we estimate to be $\ensuremath{\psi}\ensuremath{\sim}1.0$ and 2.3 in three and four dimensions, respectively. We observe the rejuvenation and memory effects in the four-dimensional sample, which, we argue, is unrelated to ``temperature chaos.'' Our discussion in terms of length scales allows us to address several experimentally relevant issues, such as superaging versus subaging effects, the role of a finite cooling rate, or the so-called Kovacs effect.

By means of Monte Carlo simulations on the three-dimensional Ising spin-glass model, we have studied aging phenomena with various temperature(

T

)-change protocols. Particularly, a

T

-shift protocol, in which a system is first quenched to and aged for a period

t_{\rm w1}

at a temperature

T_1

, and subsequently aged at a new temperature

T_2

is closely investigated. Most importantly, the mean size of domains, which is extracted from the replica-overlap function, was found to grow monotonically without any appreciable decrease by the

T

-change. We also found the relaxation of energy density and spin auto-correlation function during the

T

-shift process can be explained within the following picture: the dynamics finally crossovers to an isothermal aging of

T_2

at around

t_2 \simeq t_{\rm w1}^{\rm (eff)}

after the

T

-change, where

t_{\rm w1}^{\rm (eff)}

is an effective waiting time related with

t_{\rm w1}

, but in the transient regime

t_2 \lt t_{\rm w1}^{\rm (eff)}

, adjustment of the population of thermally active droplets from that at

T_1

T_2

takes place very slowly. Implications of the results on aging phenomena in other

T

-change protocols such as

T

-cycling and continuous

T

-change with an intermittent stop observed by simulations as well as experiments are discussed.