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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
Metastable states in spin glasses and disordered ferromagnets
1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA.
We analyze M-spin-flip stable states in disordered Ising models. Our dynamical approach reveals properties of metastable states, including their overlap distribution being a delta function at zero.
Area of Science:
- Statistical mechanics
- Condensed matter physics
- Disordered systems
Background:
- Understanding metastable states is crucial in spin glasses and ferromagnets.
- Disordered magnetic systems exhibit complex energy landscapes.
Purpose of the Study:
- To analytically study M-spin-flip stable states in disordered Ising models.
- To investigate properties of metastable states using a dynamical approach.
Main Methods:
- Dynamical analysis of a zero-temperature process with M-spin flips.
- Convergence of the dynamical process to a metastable limit.
- Examination of properties like energy, overlap, and magnetization.
Main Results:
- Characterization of M-spin-flip stable states in all dimensions and for all M.
- Demonstration that the overlap distribution of these states is a delta function at zero.
- Development of a dynamics for M=infinity to study ground state structure.
Conclusions:
- The dynamical approach provides insights into the nature and distribution of metastable states.
- The M=infinity dynamics offers a new tool for exploring ground state properties in complex magnetic systems.
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