2018 Fiscal Year Final Research Report
Improvement of dynamicsl scaling analysis by means of the kernel method and new development for the nonequilibrium relaxation method
| Project/Area Number |
15K05205
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
Ozeki Yukiyasu 電気通信大学, 大学院情報理工学研究科, 教授 (70214137)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | 非平衡緩和法 / 動的スケーリング解析 / カーネル法 / 臨界普遍性 / Kosterlitz-Thouless転移 / トポロジカル相転移 |
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| Outline of Final Research Achievements |
We succeed an improvement of the dynamical scaling by means of the kernel method, by which a scaling function can be expressed by the kernel functions avoiding some trial and error processes. An efficient and fast estimation method is realized by means of the conjugate gradient method for optimization. The process for scaling is almost automatized providing various applications. The bootstrap method by the use of huge number of data points provides a remarkable improvement for the accuracy of estimations. Comparing dynamical scaling methods with assuming several patterns for asymptotic forms of relaxation time and that without any assumption for the form, we develop a method to discriminate the transition types. We also establish the reliable analysis for topological phase transitions such as the KT one.
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| Free Research Field |
統計物理学
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| Academic Significance and Societal Importance of the Research Achievements |
相転移や臨界現象における臨界普遍性の確立は、繰り込み群の提案依頼の課題だが、確認するための道具は不十分で、近年の数値計算でも満足な結果は得られていない。シミュレーションによる臨界指数の評価は年々向上しているが、フラストレーション系、提示原型、ランダム系等では遅い緩和によりしばしば困難に直面する。非平衡緩和法はそのような状況を打破する可能性を秘めており、今回の動的スケーリングの改良による解析精度の向上と解析作業の効率化は、今後の分野の発展に大きく貢献することが期待される。
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