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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
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Phase transitions of a cluster Ising model.
1School of Science and Engineering of Mathematics and Physics, Anhui University of Technology, Maanshan, Anhui 243002, China.
Physical Review. E
|November 28, 2019
Summary
This study analyzes a cluster Ising model, revealing critical exponents for topological phase transitions. Findings detail universal scaling at ordinary critical points but note complex behaviors at multicritical points.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Quantum Phase Transitions
Background:
- The cluster Ising model with multispin interactions is exactly solvable using free fermion techniques.
- This model exhibits topological phases characterized by integer winding numbers.
Purpose of the Study:
- Investigate critical and multicritical behaviors of phase transitions between topological phases.
- Determine critical exponents governing correlation length and order parameter scaling.
Main Methods:
- Exact solution within the framework of free fermions.
- Analysis of phase transitions in a cluster Ising model.
Main Results:
- For ordinary critical points, the correlation length exponent is ν=1.
- The order parameter scaling exponent is β=ΔNw/8, where ΔNw is the winding number difference.
- Multicritical points exhibit complex behaviors, including path-dependent scaling and quasicriticality.
Conclusions:
- The study provides precise critical exponents for topological phase transitions in the cluster Ising model.
- Identified limitations of universal scaling at multicritical points, highlighting emergent complex phenomena.
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