Introducing a new simulation method using machine learning and lattice deformation

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K03773
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Shibaura Institute of Technology
• Principal Investigator: Nakamura Tota 芝浦工業大学, 工学部, 教授 (50280871)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: 格子変形 / 機械学習 / モンテカルロ法 / 相転移

Outline of Final Research Achievements

We developed a simulation method for a spin model of a magnetic material by modulating the strength of the spin-spin interaction to collectively obtain the temperature dependence of the measured physical quantities. At the same time, machine learning was used to analyze the measured physical quantities to improve the measurement accuracy near the phase transition temperature.
We applied this method to various spin models and confirmed its usefulness. The phase transition temperature and critical exponents were obtained with unprecedented accuracy for an exactly-solved model. Calculations with sufficient accuracy were achieved for models showing the Berezinskii-Kosterlitz-Thouless transition, which have been conventionally difficult to analyze.　We have also confirmed that this method is particularly effective for complex systems with incommensurate phases.

Free Research Field

物性理論

Academic Significance and Societal Importance of the Research Achievements

一様な系の解析を変形を加えた別な系で代用することができる、しかも一様系で生じていた解析の困難を緩和・解決することができる、このような野心的な試みを達成することがこの研究課題の最も重要な意義です。結果として、測定量の精度向上が確認され、解析困難系への応用の道も開けました。これまでは一様系の解析は一様系のシミュレーションで行う、という固定観念に一石を投じる成果だと言えます。従来の価値観に囚われず、そこを崩した上で新しい価値観を創造する、という意味では社会的な意義も大きいと言えます。