Precise determination of the multicritical point by renormalization group and duality analysis

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20740218
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Kyoto University (2010-2011); Tokyo Institute of Technology (2008-2009)
• Principal Investigator: OHZEKI Masayuki Tokyo Institute of Technology, 大学院・情報学研究科, 助教 (80447549)
• Project Period (FY): 2008 – 2011
• Keywords: 繰りこみ群 / スピングラス / 双対変換 / 厳密解 / 量子情報

Research Abstract

統計力学の一手法である,双対変換と繰りこみ群を合わせた新しい手法を,古典情報,量子情報の両面と関連したスピングラス模型のタ重臨界点周辺で展開させる.
応用的にも,物理学の観点から情報理論の根幹を見直す事に通じており,重要である.
(1)多重臨界点の正確な導出法の確立
(2)量子情報の誤り訂正限界との関係
(3)分配関数の対称性を利用した解析
以上の三点を中心に解析的な研究を行ってきた.

Research Products

• [Journal Article] Quantum Annealing with Jarzynski Equality Physical Review Lettres (2010)
  • Author(s): 大関真之
  • Journal Title: 105 Pages: 050401-1-050401-4
  • Peer Reviewed
• [Journal Article] Nonequilibrium Relations for Spin Glasseswith Gauge SymmetryJournal of Physical Society of Japan (2010)
  • Author(s): 大関真之、西森秀稔
  • Journal Title: 79 Pages: 084003-1-080403-4
  • Peer Reviewed
• [Journal Article] Accuracy threshold of topological colorcodes on the hexagonal andsquare-octagonal lattices (2009)
  • Author(s): 大関真之
  • Journal Title: Physical Review E 80 Pages: 011141-1-011141-4
  • Peer Reviewed
• [Journal Article] Analytical evidence for the absence ofspin glass transition on self-duallatticesJournal of Physics A : Mathematical and Theory (2009)
  • Author(s): 大関真之、西森秀稔
  • Journal Title: 42 Pages: 332001-1-3322001-10
  • Peer Reviewed
• [Journal Article] Locations of multicritical points for spinglasses on regular lattices (2009)
  • Author(s): 大関真之
  • Journal Title: Physical Review E 79 Pages: 021129-1-021129-14
  • Peer Reviewed
• [Presentation] Nonequilibrium relations in spin glasswith gauge symmetry (2011)
  • Author(s): 大関真之
  • Organizer: Internatical Meeting on Frontier in SpinGlass Theory
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-11-18
• [Presentation] ゲージ対称性とJarzynski等式によるスピングラスの平衡・非平衡解析 (2011)
  • Author(s): 大関真之
  • Organizer: 日本物理学会2010年秋季大会
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2011-09-25
• [Presentation] 高次元干渉通信路とランダム磁場イジング模型の相転移現象 (2011)
  • Author(s): 大関真之
  • Organizer: 日本物理学会第66回年次大会
  • Place of Presentation: 新潟大学
  • Year and Date: 2011-03-28
• [Presentation] Nonequilibrium work distribution inquantum annealing (2011)
  • Author(s): 大関真之
  • Organizer: The third international workshop onDynamics and Manipulation of Quantum Systems
  • Place of Presentation: 東京大学
  • Year and Date: 2011-02-14
• [Presentation] Nonequilibrium work distribution inquantum annealing (2011)
  • Author(s): 大関真之
  • Organizer: International Symposium "Nanoscience andQuantum Physics 2011"
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-01-26
• [Book] 日本物理学会誌 66 (2011)
  • Author(s): 大関真之、西森秀稔
  • Total Pages: 252-254
  • Publisher: 量子アニーリング
• [Book] 物性研究 94(4) (2010)
  • Author(s): 大関真之
  • Total Pages: 440-527
  • Publisher: スピングラス模型の臨界点と双対変換～厳密解を求めて～