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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Renormalization group study of random quantum magnets.
István A Kovács1, Ferenc Iglói
1Department of Physics, Loránd Eötvös University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary. ikovacs@szfki.hu
Journal of Physics. Condensed Matter : an Institute of Physics Journal
|September 21, 2011
Summary
Researchers developed an efficient algorithm to study random quantum magnets. The strong disorder renormalization group method reveals that disorder dominates quantum fluctuations at critical points.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Quantum Magnetism
Background:
- The random transverse field Ising model is a key model for understanding random quantum magnets.
- Studying critical behavior in such systems is computationally challenging.
Purpose of the Study:
- To develop an efficient numerical algorithm for the strong disorder renormalization group method.
- To investigate the critical behavior of the random transverse field Ising model on various graph structures.
- To analyze Griffiths singularities in different phases.
Main Methods:
- Developed a highly efficient numerical algorithm for the strong disorder renormalization group method.
- Applied the algorithm to N-site clusters up to N ~ 4x10^6.
- Studied systems on regular lattices (D <= 4) and Erdős-Rényi random graphs (infinite dimensional).
Main Results:
- Quantum critical behavior is governed by an infinite disorder fixed point where disorder dominates quantum fluctuations.
- The renormalization procedure and critical properties are asymptotically exact for large systems.
- Griffiths singularities were observed in paramagnetic and ferromagnetic phases.
Conclusions:
- Disorder plays a crucial role in the critical behavior of random quantum magnets.
- The developed algorithm provides accurate insights into large-scale quantum critical phenomena.
- The numerical method is adaptable for studying other random quantum systems.
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