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Scale invariance in disordered systems: the example of the random-field Ising model
Giorgio Parisi1, Nicolas Sourlas
1Dipartimento di Fisica, INFM, SMC and INFN, Università di Roma La Sapienza, P. A. Moro 2, Italy.
Physical Review Letters
|December 18, 2002
Summary
Numerical simulations reveal strong fluctuations in the 3D random-field Ising model (RFIM). Finite-volume correlation lengths are not self-averaging due to bound states, a phenomenon potentially common in disordered systems.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Disordered Systems
Background:
- The random-field Ising model (RFIM) is a key model for studying magnetic materials with quenched disorder.
- Understanding the behavior of the correlation function in critical regions is crucial for characterizing phase transitions.
Purpose of the Study:
- To investigate the nature of fluctuations in the correlation function of the 3D RFIM at criticality.
- To determine if the correlation length is self-averaging in finite volumes for this model.
Main Methods:
- Numerical simulations were employed to study the 3D RFIM.
- Analysis focused on the correlation function and correlation length in critical regions.
Main Results:
- The correlation function of the 3D RFIM exhibits very strong fluctuations at criticality.
- In finite volumes, the correlation length is found to be non-self-averaging.
- This behavior is attributed to the formation of a bound state in the underlying field theory.
Conclusions:
- The non-self-averaging of correlation length in finite volumes is a significant finding for the 3D RFIM.
- This nonperturbative phenomenon is likely generic for 2D disordered systems and potentially other 3D disordered systems.
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