Conformal bootstrap method and critical phenomena

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K05491
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Okinawa Institute of Science and Technology Graduate University
• Principal Investigator: Hikami Shinobu 沖縄科学技術大学院大学, 数理理論物理学ユニット, 教授 (30093298)
• Co-Investigator(Kenkyū-buntansha): 島田 悠彦 津山工業高等専門学校, 総合理工学科, 特命助教 (20751192)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: くりこみ群 / 共形場理論 / 超対称性

Outline of Final Research Achievements

Critical phenomena with critical exponents, which measure the degree of divergences, are know to be universal. In two dimensions, some are obtained exactly but 3 dimensional Ising case, it is not obtained exactly. Recently conformal bootstrap method is proposed, and it provides very accurate numerical values of the critical exponents for 3 dimensional Ising model. We applied this method to polymer case, and found rather good values, The determinant method also can be applied, and we investigated the supersymmetric cases by this bootstrap method.

Free Research Field

数理物理学

Academic Significance and Societal Importance of the Research Achievements

臨界指数を正確に求めることは、ゆらぎの物理現象を正しく理解することに繋がり、実験を説明できる理論を構築する上で重要なことである.得られた結果は共形場ブートストラップ法が有効であることを示し、今後の理論の重要な方向を示すものである.