Violation of the fluctuation dissipation relation in a spin glass

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Violation of the fluctuation dissipation relation
in a spin glass

• Federico Romá
• Sebastián Bustingorry
• Daniel Domínguez
• Pablo M. Gleiser
• Centro Atómico Bariloche
• Argentina

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Outline

• The ?J Edwards-Anderson (?J EA) spin glass model
• Violation of the fluctuation dissipation theorem
  
  
• Some conclusions and a lot of open questions...

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The ?J EA spin glass model
2D Lattice
Backbone
Solidary Spins
The ground state of the EA model is degenerate.
The backbone is defined as the set of bonds
which are always satisfied or always frustrated
in all ground state configurations. Solidary
spins are the spins in the backbone.
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Backbone of the ?J EA model
3D, Tc 1.12
2D, Tc 0
The backbone percolates 75 of the spins are
solidary spins
The backbone does not percolate 67 of the spins
are solidary spins
F. Romá et al, Physica A 363, 327 (2006). F. Romá
et al, Phys. Rev. B 75 020402(R) (2007).
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Dynamical Heterogeneities in the ?J EA
Pln(t) Mean flipping time distribution,
Tc 1.12
Romá, Bustingorry y Gleiser, Phys. Rev. Lett 96,
167205 (2006)
F. Ricci-Tersenghi y R. Zecchina, Phys. Rev. E
62, R7567 (2000).
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Fluctuation Dissipation Theorem FDT
Relates equilibrium thermal fluctuations with the
response of the system to a small perturbation.
A. Crisanti y F. Ritort, Reviews of Modern
Physics 2003
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Violation of FDT in spin glass
Experiments
Edwards-Anderson model
c
tw
TltTc1.12
F. Ricci-Tersenghi, Phys. Rev. E (2003)
D. Hérisson y M. Ocio, EPJB (2004)
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Violation of the FDT, 3D ?J EA spin glass
We measure single spin observables
in terms of this local quantity we can define the
global correlation
in the same way the integrated response function
can be defined as
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Dynamical heterogeneities in the Violation of the
FDT, 3D ?J EA spin glass
N 203
The dynamical heterogeneities are obtained
averaging over 50 different disorder
configurations and also over 104 thermal
histories for each disorder configuration.
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Violation of the FDT, 3D ?J EA spin glass
We need a large number of samples for which
ground state information is known. This limits
the largest system sizes to N 83
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Violation of the FDT, 3D ?J EA spin glass
The rest of spins
Largest island of solidary spins
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Gauge Transformation
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Gauge Transformation
Largest island of solidary spins after the Gauge
transformation
Largest island of solidary spins before the Gauge
transformation
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Gauge Transformation
Largest island of solidary spins after the Gauge
transformation
We find that about 10 of the bonds are
frustrated in the largest island of
solidary spins.
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Violation of FDT
The system divided in two sets A y B
The whole system
A Solidary spins in the largest island of the
backbone B All the rest....
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Conclusions

• We study the violation of the fluctuation
  dissipation relation in the EA J 3D model. We
  find dynamical heterogeneities which persist even
  when disorder
• over disorder configurations are taken into
  account.
• We show that there is a relation between the
  backbone and the dynamical heterogeneities.
• We show that a fraction of the system presents
• a violation of FDT reminiscent of a
  ferromagnetic systems while the other fraction
  seems to
• equilibrate.
• Results to appear in PRL (2007)
  cond-mat/0608603.

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Violación de FDT, un ejemplo coarsening Ising
ferromagnético 3D, N 803
T 2.5 lt Tc ? 4.5

tw 100
tw
tw 1500
A. Barrat, Phys. Rev. E 57, 3629 (1998)