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Updated: May 31, 2026
08:55
Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Real-space renormalization group for the transverse-field Ising model in two and three dimensions
Ryoji Miyazaki1, Hidetoshi Nishimori, Gerardo Ortiz
1Department of Physics, Tokyo Institute of Technology, Megro-ku, Tokyo, Japan.
Summary
This study applies a real-space renormalization-group method to analyze transverse-field Ising models. The method accurately estimates critical exponents in two and three dimensions, aligning with classical Ising models.
Area of Science:
- Statistical physics
- Condensed matter physics
Background:
- The transverse-field Ising model is a fundamental model in statistical mechanics.
- Real-space renormalization-group methods offer a powerful tool for analyzing critical phenomena.
Purpose of the Study:
- To generalize a real-space renormalization-group method for analyzing two- and three-dimensional transverse-field Ising models.
- To accurately determine critical exponents for these models.
Main Methods:
- The study employs a generalized real-space renormalization-group method.
- This method exploits the exact invariance of the model under renormalization.
Main Results:
- Accurate critical exponent ν values were obtained for two- and three-dimensional models.
- These results show good agreement with values for classical Ising models in higher dimensions.
Conclusions:
- The real-space renormalization-group method provides accurate estimates for critical exponents.
- This represents a significant advancement in applying renormalization-group techniques to higher-dimensional lattice models.
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