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

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.

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.

2．Model ・ ・

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

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

Outline of simulations 3D 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 :

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.

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

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

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

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

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

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

Estimation of the overlap length 3D 4D

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

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

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

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

Result （L=16,3D)

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

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

Finite size scaling of ４D ３D

Comparison with other results 3D 4D If we are measuring peculiar observables which are not related to the bulk property of the model, we can not expect such agreements.

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/0411138