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Chaos in temperature in the Sherrington-Kirkpatrick model
1Dipartimento di Scienze Fisiche, Università "Federico II," Complesso Monte S. Angelo, I-80126 Napoli, Italy. tommaso.rizzo@inwind.it
Physical Review Letters
|April 12, 2003
Summary
We demonstrate temperature chaos in the Sherrington-Kirkpatrick model, a minuscule effect found in the ninth order of perturbation theory. This research analyzes systems at varying temperatures to understand overlap distribution functions in finite systems.
Area of Science:
- Statistical mechanics
- Condensed matter physics
- Theoretical physics
Background:
- The Sherrington-Kirkpatrick (SK) model is a fundamental model in statistical mechanics for spin glasses.
- Understanding the behavior of complex systems under varying thermodynamic conditions is crucial.
- Perturbation theory is a key analytical tool for approximating solutions in physics.
Purpose of the Study:
- To prove the existence of temperature chaos in the Sherrington-Kirkpatrick model.
- To investigate the impact of differing temperatures on system overlap.
- To analyze the overlap distribution function in finite-size systems.
Main Methods:
- Analytical study of equations governing two systems at different temperatures with fixed overlap.
- Numerical simulations to complement analytical findings.
- Perturbation theory up to the ninth order to quantify the effect.
Main Results:
- Existence of temperature chaos demonstrated in the SK model.
- The effect of temperature chaos is exceedingly small, appearing at the ninth order of perturbation theory.
- Information on the behavior of the overlap distribution function P(T1,T2)(q) in finite-size systems was obtained.
Conclusions:
- Temperature chaos is a real phenomenon in the Sherrington-Kirkpatrick model, albeit very subtle.
- The study provides insights into the complex thermodynamic behavior of spin glass models.
- The findings contribute to the understanding of statistical mechanics in disordered systems.