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Magnetic field chaos in the Sherrington-Kirkpatrick model
Alain Billoire1, Barbara Coluzzi
1Service de Physique Théorique CEA-Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette, France.
Summary
This study reveals magnetic field chaos in the Sherrington-Kirkpatrick model, even at moderate sizes. This chaos is detectable using a modified Parallel Tempering algorithm, unlike temperature chaos.
Area of Science:
- Statistical mechanics
- Condensed matter physics
Background:
- The Sherrington-Kirkpatrick (SK) model is a fundamental model in statistical mechanics for studying spin glasses.
- Understanding the phase diagram and chaotic behavior within the SK model is crucial for theoretical physics.
Purpose of the Study:
- To investigate the presence and characteristics of magnetic field chaos in the Sherrington-Kirkpatrick model.
- To compare the detectability of magnetic field chaos versus temperature chaos for varying system sizes.
Main Methods:
- Utilized a modified Parallel Tempering algorithm allowing movement between different magnetic field values (h).
- Analyzed the probability distribution of the overlap between two replicas at distinct magnetic fields (h(0) and h(1)).
Main Results:
- Observed clear evidence of magnetic field chaos in the SK model at moderate system sizes.
- Magnetic field chaos was detectable, whereas temperature chaos remained unobservable within current thermalization limits.
Conclusions:
- The modified Parallel Tempering approach effectively reveals magnetic field chaos in the SK model.
- Magnetic field chaos is a more prominent feature at moderate system sizes than temperature chaos.