1. M. Sasaki, K. Hukushima, H. Yoshino, H. Takayama
Fragility of the Equilibrium State in the Edwards-Anderson Ising Spin Glass
M. Sasaki, K. Hukushima,
H. Yoshino, H. Takayama

2. 1. Introduction Spin glass : A state that each spin is frozen
in random direction.
Temperature chaos : The frozen pattern changes
with temperature.
Temperature chaos has great interest because
of its potential relevance for rejuvenation in
aging phenomena.
2. However, it is not still clear whether
temperature chaos exists in spin glasses or not.

3. We have investigated this problem by measuring domain-wall free-energy and related observables in the EA spin glass model.
The existence of temperature chaos in this model.

4. 2．Model ・ ・

5. Ovserbable I :
Domain-wall Free-energy
(effective coupling
between block spins)
If there exists temperature chaos, δF should
depend on temperature chaotically.

6. Ovserbable II : Domain-wall energy
Ovserbable III : Domain-wall entropy

7. Outline of simulations3D
size : L=4, 6, 8, 10, 12, 14, 16
number of samples : around 1500
temperature range : 4D
size : L=4, 5, 6, 7, 8, 10
number of samples : around 1500 (820 for L=10)
temperature range :

8. Oscillation becomes stronger with increasing L.
Result of 10 samples (3D)
L=4
L=8
L=12
L=16
Oscillation becomes stronger with increasing L.
and chancel with each other.

9. Result of 10 samples (4D)
L=4
L=6
L=8
L=10

10. Size dependence of increases more rapidly than does. ３D ４D T=0.4J

11. estimated by two different ways.
４D、L=10

12. Temperature dependence of δF is totally chaotic in this limit.
In the limit L→∞,
Temperature dependence of δF is
totally chaotic in this limit.

13. Correlation decays faster with increasing L.
Correlation function of ３D 4D
T=0.4J
T=0.6J
Correlation decays faster with increasing L.

14. Scaling plot of ３D ４D
Even if the temperature difference is very small,
δFs at two different temperatures are
decorrelated completely.

15. Estimation of the overlap length3D 4D

16. + Quantitative estimation Quantitative estimation of the domain size
of the overlap length
Quantitative study to reveal the relation
between temperature chaos and rejuvenation.

17. Domain wall motion caused by temperature chaos (3D only)
Replica A
Replica B
Upper spins :
Lower spins :

18. Domain wall = The surface where
changes its sign.
However, it is not easy to display it directly.

19. Idea I : Display the observable
Idea II : Display
Idea I : Display the observable
DW seems to move to the
center as T increases.
（∵ 　　 ）
One defect x y

20. Result （L=16,3D)

21. Relation between the domain wall motion and the observables
The relation is not so clear at the moment.

22. Q : Are these results due to this somewhat
peculiar boundary condition?

23. Finite size scaling of ４D ３D

24. Comparison with other results3D 4D
If we are measuring peculiar observables which
are not related to the bulk property of the model,
we can not expect such agreements.

25. M. Sasaki, K. Hukushima, H. Yoshino and H. Takayama
Conclusion
We have found several strong evidences for temperature chaos in the EA spin glass by measuring domain-wall free-energy and related observables.
We have estimated the overlap length of the EA spin glass quantitatively.
We have directly observed domain wall motion caused by temperature chaos.
M. Sasaki, K. Hukushima, H. Yoshino and H. Takayama
cond-mat/