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

Numerical and experimental studies of the dynamics of Ising spin glasses

Jan‐Olov Andersson

Jan 1, 19941 citation

Field-Shift Aging Protocol on 3D Ising Spin-Glass Model: Dynamical Crossover between the Spin-Glass and Paramagnetic States

Hajime Takayama, Koji Hukushima

Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model under a static magnetic field $h$ are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature $T$ . For each process with $(T; \tw, h)$, $\tw$ being the waiting time before the field is switched on, we extract the dynamical crossover time, $\tcr(T; \tw, h)$. We have found a nice scaling relation between the two characteristic length scales which are properly determined from $\tcr$ and $\tw$ and then are normalized by the static field crossover length introduced in the SG droplet theory. This scaling behavior implies the instability of the SG phase in the equilibrium limit even under an infinitesimal $h$ . In comparison with this numerical result the field effect on real spin glasses is also discussed.Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model under a static magnetic field $h$ are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature $T$. For each process with $(T; \tw, h)$, $\tw$ being the waiting time before the field is switched on, we extract the dynamical crossover time, $\tcr(T; \tw, h)$. We have found a nice scaling relation between the two characteristic length scales which are properly determined from $\tcr$ and $\tw$ and then are normalized by the static field crossover length introduced in the SG droplet theory. This scaling behavior implies the instability of the SG phase in the equilibrium limit even under an infinitesimal $h$. In comparison with this numerical result the field effect on real spin glasses is also discussed.

arXiv:cond-mat/0307641Journal of the Physical Society of JapanAug 15, 200430 citations

Aging Phenomena in Ising Spin Glasses in Magnetic Field

Hajime Takayama, Petra E. Jönsson

The aging phenomena in Ising spin glasses in a magnetic field are investigated both by the numerical simulation on three-dimensional Ising Edwards-Anderson model and by the experiment on the Fe0.55Mn0.45TiO3 Ising spin glass. After reviewing our recent numerical work on the field-shift aging protocol, by which we argue that the spin-glass (SG) phase is unstable in a static magnetic field of any strength, we present the nonequilibrium aspects of the field-cooled magnetization in a relatively small field observed numerically and experimentally. The results are compatible with the absence of the equilibrium SG phase in a field.The aging phenomena in Ising spin glasses in a magnetic field are investigated both by the numerical simulation on three-dimensional Ising Edwards-Anderson model and by the experiment on the Fe0.55Mn0.45TiO3 Ising spin glass. After reviewing our recent numerical work on the field-shift aging protocol, by which we argue that the spin-glass (SG) phase is unstable in a static magnetic field of any strength, we present the nonequilibrium aspects of the field-cooled magnetization in a relatively small field observed numerically and experimentally. The results are compatible with the absence of the equilibrium SG phase in a field.

Progress of Theoretical Physics SupplementJan 1, 20050 citations

Aging Relation for Ising Spin Glasses

之康尾関, Yukiyasu Ozeki

Jan 1, 19970 citations

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.

Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model under a static magnetic field

h

are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature

T

. For each process with $(T; \tw, h)$, $\tw$ being the waiting time before the field is switched on, we extract the dynamical crossover time, $\tcr(T; \tw, h)$. We have found a nice scaling relation between the two characteristic length scales which are properly determined from $\tcr$ and $\tw$ and then are normalized by the static field crossover length introduced in the SG droplet theory. This scaling behavior implies the instability of the SG phase in the equilibrium limit even under an infinitesimal

h

. In comparison with this numerical result the field effect on real spin glasses is also discussed.