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Updated: Jul 3, 2026
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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
Multicritical points for spin-glass models on hierarchical lattices
Masayuki Ohzeki1, Hidetoshi Nishimori, A Nihat Berker
1Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo, Japan.
Summary
This study numerically investigates multicritical points on hierarchical lattices. An improved analytical conjecture, informed by renormalization group methods, offers more precise predictions than previous theories.
Area of Science:
- Statistical mechanics
- Condensed matter physics
- Computational physics
Background:
- Multicritical points govern phase transitions in complex systems.
- Hierarchical lattices exhibit unique scaling properties.
- Existing analytical methods provide approximate locations for these points.
Purpose of the Study:
- To numerically determine the precise locations of multicritical points on hierarchical lattices.
- To compare numerical findings with existing analytical conjectures.
- To develop an improved analytical conjecture for more accurate predictions.
Main Methods:
- Renormalization group analysis was employed for numerical investigation.
- Duality, gauge symmetry, and replica methods were used for analytical conjecture.
- Comparison between numerical data and analytical predictions was performed.
Main Results:
- The conventional analytical conjecture yields locations slightly deviating from numerical data.
- A new, improved conjecture is proposed based on renormalization group insights.
- The improved conjecture shows high consistency with extensive numerical results.
Conclusions:
- The conventional analytical conjecture for multicritical points is not exact.
- Renormalization group analysis provides a more reliable approach for locating these points.
- The proposed improved conjecture offers significantly enhanced predictive accuracy for multicritical phenomena.
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