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Random-field and random-anisotropy O(N) spin systems with a free surface
1Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Unité Mixte de Recherche No 5672 Associée au Centre National de la Recherche Scientifique, 46 Allée d'Italie, 69007 Lyon, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
We investigated surface scaling in disordered O(N) spin systems. Our functional renormalization group approach reveals surface scaling laws for transitions and quasi-long-range order, applicable to various disordered systems.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Surface Science
Background:
- O(N) spin systems exhibit critical phenomena and phase transitions influenced by dimensionality and disorder.
- Disorders like random fields and anisotropies significantly alter system behavior, especially near surfaces.
- Understanding surface scaling is crucial for characterizing phase transitions in finite systems.
Purpose of the Study:
- To investigate the surface scaling behavior of a semi-infinite d-dimensional O(N) spin system with quenched random field and random anisotropy disorders.
- To derive surface scaling laws for both ordinary surface transitions above the lower critical dimension and quasi-long-range order below it.
- To calculate the corresponding surface exponents to one-loop order.
Main Methods:
- Utilizing a functional renormalization group (FRG) approach.
- Analyzing the behavior of O(N) spin systems in d dimensions with quenched disorder.
- Calculating surface exponents to one-loop order.
Main Results:
- Derived surface scaling laws describing ordinary surface transitions for d > d(LC) = 4.
- Characterized the long-range behavior of spin correlations near the surface in the quasi-long-range-order phase for d < d(LC).
- Calculated surface exponents to one-loop order for both regimes.
Conclusions:
- The study provides a unified framework for understanding surface scaling in disordered O(N) spin systems across different dimensionalities.
- The derived scaling laws and exponents are applicable to diverse physical systems, including elastic systems, amorphous magnets, and Helium-3.
- This work advances the understanding of critical phenomena at surfaces in the presence of quenched disorder.
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