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Domain statistics in a finite Ising chain.
1Department of Mechanics and Mathematics, Sumy State University, 2, Rimskiy-Korsakov Street, 40007 Sumy, Ukraine. denisov@sumdu.edu.au
Summary
This study details statistical properties of finite Ising chains, providing probability functions for domain structures. These findings help characterize magnetism in nanoscale materials and memory devices.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- Understanding magnetism in finite systems is crucial for nanoscale applications.
- Ising models provide a fundamental framework for studying magnetic phenomena.
Purpose of the Study:
- To statistically analyze the domain structure of a finite Ising chain.
- To derive probability functions for domain-related variables.
- To establish criteria for ferromagnetic-like behavior in finite chains.
Main Methods:
- Extensive combinatorics were employed to derive probability functions.
- Calculated averages and variances for key statistical properties.
- Analyzed low-temperature behavior and transition times.
Main Results:
- Obtained one-variable probability functions for domain walls, up domains, and spin counts within domains.
- Calculated averages and variances for these distributions.
- Defined a criterion for ferromagnetic-like behavior in finite Ising chains.
Conclusions:
- The statistical properties of finite Ising chains are well-defined by derived probability functions.
- The study provides a method to characterize magnetism in finite systems.
- Results are applicable to monatomic metal wires and atomic-scale memory devices.