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

• 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 京都大学, 大学院・情報学研究科, 助教 (80447549)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 繰りこみ群 / スピングラス / 双対変換 / 厳密解 / 量子情報 / 量子情報誤り訂正 / Jarzynski等式 / 多重臨界点 / 最適化問題 / 誤り訂正符号 / 統計力学 / 相転移 / ランダムスピン

Research Abstract

We develop the classical methods in statistical mechanics, duality and renormalization group analysis such that they are applicable to both of the classical and quantum information theory through the special critical point in spin glasses. The study is closely associated with reconsideration of information theory through physics. We perform the following analytical studies ; 1. Establishment to identify the location of the special critical point 2. Consideration on the relationship with the error threshold in quantum information 3. Analysis by aid of the symmetry of the partition function We obtain many outstanding results until the final term of the period supported by the foundation.
1. Establishment to identify the location of the special critical point
2. Consideration on the relationship with the error threshold in quantum information
3. Analysis by aid of the symmetry of the partition function
We obtain many outstanding results until the final term of the period supported by the foundation.

Research Products

• [Journal Article] Nonequilibrium work on spin glasses in transverse and random fields (2011)
  • Author(s): 大関真之、勝田仁之、西森秀稔
  • Journal Title: Journal of Physical Society of Japan Volume: 80
  • Peer Reviewed
• [Journal Article] Jarzynski equality for an energy-controlled system (2011)
  • Author(s): 大関真之、勝田仁之
  • Journal Title: Journal of Physical Society of Japan Volume: 80
  • NAID: 210000109000
  • Peer Reviewed
• [Journal Article] Universality in phase boundary slopes for spin glasses on self dual lattices (2011)
  • Author(s): 大関真之、Creighton K. Thomas、Helmut G Katzgraber、Hector Bombin、Miguel Angel Martin-Delgado
  • Journal Title: Journal of Statistical Mechanics
  • NAID: 120002970860
  • Peer Reviewed
• [Journal Article] Quantum annealing : An introduction and new developments (2011)
  • Author(s): 大関真之、西森秀稔
  • Journal Title: Journal of Computational and Theoretical Nanoscience Volume: 8 Pages: 963-971
  • Peer Reviewed
• [Journal Article] Nonequilibrium Work on Spin Glasses in Longitudinal and Transverse Fields (2011)
  • Author(s): 大関真之、勝田仁之、西森秀稔
  • Journal Title: Journal of the Physical Society of Japan Volume: 80 Issue: 8 Pages: 084002-084002
  • DOI: 10.1143/jpsj.80.084002
  • NAID: 40018947218
  • Peer Reviewed
• [Journal Article] Nonequilibrium work performed in quantum annealing (2011)
  • Author(s): 大関真之、西森秀稔
  • Journal Title: Journal of Physics : Conference Series Volume: 302 Pages: 012047-012047
  • DOI: 10.1088/1742-6596/302/1/012047
  • Peer Reviewed
• [Journal Article] Jarzynski Equality for an Energy-Controlled System (2011)
  • Author(s): 勝田仁之、大関真之
  • Journal Title: Journal of Physics : Conference Series Volume: 302 Pages: 012048-012048
  • DOI: 10.1088/1742-6596/302/1/012048
  • NAID: 210000109000
  • Peer Reviewed
• [Journal Article] Quantum annealing with Jarzynski equakity (2011)
  • Author(s): 大関真之、西森秀稔
  • Journal Title: Computer Physics Communications Volume: 182 Pages: 257-259
  • Peer Reviewed
• [Journal Article] Nonequilibrium relations in spin glasses (2011)
  • Author(s): 大関真之、西森秀稔
  • Journal Title: Physica E : Low-dimensional Systems and Nanostructures Volume: 43 Pages: 782-785
  • Peer Reviewed
• [Journal Article] Zero-temperature complex replica zeros of the±J Ising spinglass on mean-field systems and beyond (2011)
  • Author(s): 小渕智之、樺島祥之、西森秀稔、大関真之
  • Journal Title: Physica E : Low-dimensional Systems and Nanostructures Volume: 43 Pages: 786-789
  • Peer Reviewed
• [Journal Article] Extending Jarzynski equality in general Langevin system (2011)
  • Author(s): 杉山友規、大関真之
  • Journal Title: Physica E : Low-dimensional Systems and Nanostructures Volume: 43 Pages: 790-793
  • Peer Reviewed
• [Journal Article] Universality in phase boundary slopes for spin glasses on self-dual lattices (2011)
  • Author(s): 大関真之、C.K.Thomas、H.G.Katzgraber、H.Bombin、M.A.Martin-Delgado
  • Journal Title: Journal of Statistical Physics : Theory and Experiment Volume: Februray
  • NAID: 120002970860
  • Peer Reviewed
• [Journal Article] Jarzynski equality for an energy-controlled system (2011)
  • Author(s): 勝田仁之、大関真之
  • Journal Title: Journal of Physical Society of Japan Volume: 80
  • NAID: 210000109000
  • Peer Reviewed
• [Journal Article] Quantum Annealing with Jarzynski Equality Physical Review Lettres (2010)
  • Author(s): 大関真之
  • Volume: 105
  • Peer Reviewed
• [Journal Article] Nonequilibrium Relations for Spin Glasses with Gauge Symmetry (2010)
  • Author(s): 大関真之、西森秀稔
  • Journal Title: Journal of Physical Society of Japan Volume: 79 Pages: 840031-4
  • NAID: 40017245109
  • Peer Reviewed
• [Journal Article] Quantum Annealing with Jarzynski Equality Physical Review Lettres (2010)
  • Author(s): 大関真之
  • Journal Title: 105
  • 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
  • Peer Reviewed
• [Journal Article] スピングラス模型の臨界点と双対変換～厳密解を求めて～ (2010)
  • Author(s): 大関真之
  • Journal Title: 物性研究 Volume: 94
  • NAID: 110007657799
• [Journal Article] Multicritical point of spin glasses (2010)
  • Author(s): 西森秀稔、大関真之
  • Journal Title: Physica A : Statistical Mechanics and its Applications Volume: 389 Pages: 2907-2910
  • Peer Reviewed
• [Journal Article] Nonequilibrium Relations for Spin Glasses with Gauge Symmetry (2010)
  • Author(s): 大関真之、西森秀稔
  • Journal Title: Journal of Physiscal Society of Japan Volume: 79
  • NAID: 40017245109
  • Peer Reviewed
• [Journal Article] Quantum annealing with Jarzynski equality (2010)
  • Author(s): 大関真之
  • Journal Title: Physical Review Letters Volume: 105
  • Peer Reviewed
• [Journal Article] Accuracy threshold of topological color codes on the hexagonal and square-octagonal lattices (2009)
  • Author(s): 大関真之
  • Journal Title: Physical Review E Volume: 80
  • Peer Reviewed
• [Journal Article] Analytical evidence for the absence of spin glass transition on self-dual lattices (2009)
  • Author(s): 大関真之、西森秀稔
  • Journal Title: Journal of Physics A : Mathematical and Theory Volume: 42
  • Peer Reviewed
• [Journal Article] Locations of multicritical points for spin glasses on regular lattices (2009)
  • Author(s): 大関真之
  • Journal Title: Physical Review E Volume: 79
  • 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
  • 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
  • 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
  • Peer Reviewed
• [Journal Article] Analytical evidence for the absence of spin glass transition on self-dual lattices (2009)
  • Author(s): 大関真之, 西森秀稔
  • Journal Title: Journal of Physcs A : Math.Theor. 42 Pages: 332001-332001
  • Peer Reviewed
• [Journal Article] Accuracy threshold of topological color codes on the hexagonal and square-octagonal lattices (2009)
  • Author(s): 大関真之
  • Journal Title: Phys.Rev.E 80 Pages: 11141-11141
  • Peer Reviewed
• [Journal Article] Locations of multicritical points fer spin glasses on regular lattices (2009)
  • Author(s): 大関真之
  • Journal Title: Physical Review E 79 Pages: 21129-21129
  • Peer Reviewed
• [Journal Article] Multicritical points for the spin glass models on hierarchical lattices (2008)
  • Author(s): 大関真之, 西森秀稔, A. Nihat Berker
  • Journal Title: Physical Review E 77 Pages: 61116-61116
  • Peer Reviewed
• [Presentation] Nonequilibrium work relation in macroscopic system (2012)
  • Author(s): 杉山雄規、大関真之
  • Organizer: Rejuvenating Concepts in Glass Physics
  • Place of Presentation: Institut Henri Poincare (Paris)
  • Year and Date: 2012-12-15
• [Presentation] Population annealing with gauge symmetry and its application (2012)
  • Author(s): 大関真之
  • Organizer: Rejuvenating Concepts in Glass Physics
  • Place of Presentation: Institut Henri Poincare
  • Year and Date: 2012-03-31
• [Presentation] Population annealing with gauge symmetry and its application (2012)
  • Author(s): 大関真之
  • Organizer: Rejuvenating Concepts in Glass Physics
  • Place of Presentation: Institut Henri Poincare (Paris)
  • Year and Date: 2012-03-30
• [Presentation] 有限次元スピングラスの理解に向けて:ベーテ近似とその発展 (2012)
  • Author(s): 大関真之
  • Organizer: Rejuvenating Concepts in Glass Physics
  • Place of Presentation: Institut Henri Poincare (Paris)
  • Year and Date: 2012-03-30
• [Presentation] スピングラスの理論 (2012)
  • Author(s): 大関真之
  • Organizer: 日本物理学会第67回年次大会
  • Place of Presentation: 関西学院大学
  • Year and Date: 2012-03-25
• [Presentation] スピングラスの理論 (2012)
  • Author(s): 大関真之
  • Organizer: 日本物理学会第67回年次大会
  • Place of Presentation: 関西学院大学(兵庫)
  • Year and Date: 2012-03-25
• [Presentation] Population annealing with gauge symmetry against critical slowing down (2012)
  • Author(s): 大関真之
  • Organizer: East Asia Joint Symposia on Statistical Physics
  • Place of Presentation: 蘇州大学(蘇州)
  • Year and Date: 2012-03-19
• [Presentation] Population annealing with gauge symmetry against critical slowing down (2012)
  • Author(s): 大関真之
  • Organizer: East Asia Joint Symposia on Statistical Physics
  • Place of Presentation: 蘇州大学
  • Year and Date: 2012-03-09
• [Presentation] Jarzynski equality for spin glasses and its application (2012)
  • Author(s): 大関真之
  • Organizer: APS March Meeting 2012
  • Place of Presentation: Boston Convention Center (Boston)
  • Year and Date: 2012-02-29
• [Presentation] Population annealing with gauge symmetry against critical slowing down (2011)
  • Author(s): 大関真之
  • Organizer: Unifying concepts in glass physics V
  • Place of Presentation: Institut Henri Poincare (Paris)
  • Year and Date: 2011-12-15
• [Presentation] Nonequilibrium work relation in macroscopic system (2011)
  • Author(s): 杉山雄規、大関真之
  • Organizer: Unifying concepts in glass physics V
  • Place of Presentation: Institut Henri Poincare (Paris)
  • Year and Date: 2011-12-15
• [Presentation] Nonequilibrium relations in spin glass with gauge symmetry (2011)
  • Author(s): 大関真之
  • Organizer: Internatical Meeting on Frontier in Spin Glass Theory
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-11-18
• [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] 磁気記録の読み出しと相転移現象 (2011)
  • Author(s): 大関真之、田中利幸
  • 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] 横磁場Blume-Emery-Griffithsスピングラス模型の実空間繰り込み群による解析 (2011)
  • Author(s): 長内敦樹、大関真之、西森秀稔
  • 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: 2011-09-23
• [Presentation] Quantum computing by weighting (2011)
  • Author(s): 大関真之
  • Organizer: Statistical Physics of Quantum Systems
  • Place of Presentation: 東京大学
  • Year and Date: 2011-08-06
• [Presentation] Nonequilibrium relations in spin glasses (2011)
  • Author(s): 大関真之、西森秀稔
  • Organizer: The 24rd international conference on Statistical physics of the international union for pure and applied physics
  • Place of Presentation: Convention centre, Cairns, Australia
  • Year and Date: 2011-07-20
• [Presentation] Real-space renormalization group analysis of transverse field Blume-Emery-Griffiths model (2011)
  • Author(s): 長内敦樹、大関真之、西森秀稔
  • Organizer: The 24rd international conference on Statistical physics of the international union for pure and applied physics
  • Place of Presentation: Convention centre, Cairns, Australia
  • Year and Date: 2011-07-20
• [Presentation] Jarzynski equality for an energy-controlled system (2011)
  • Author(s): 勝田仁之、大関真之
  • Organizer: The 24rd international conference on Statistical physics of the international union for pure and applied physics
  • Place of Presentation: Convention centre, Cairns, Australia
  • Year and Date: 2011-07-20
• [Presentation] Duality method for identifying optimal error threshold (2011)
  • Author(s): 大関真之
  • Organizer: Quantum Information meets Statistical Mechanics
  • Place of Presentation: El Escorial Summer School (Escorial)
  • Year and Date: 2011-07-14
• [Presentation] Duality analysis in spin glasses (2011)
  • Author(s): 大関真之
  • Organizer: Complexity, Computation, Information, StatPhysHK
  • Place of Presentation: Hong Kong Baptist University, HongKong SAR, China
  • Year and Date: 2011-07-14
• [Presentation] Quantum annealing with Jarzynski equality (2011)
  • Author(s): 大関真之、西森秀稔
  • Organizer: CREST2010, International Symposium on Physics of Quantum Technology
  • Place of Presentation: 一ツ橋記念ホール、東京
  • Year and Date: 2011-04-06
• [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] 非平衡関係式を用いたポピュレーションアニーリング (2011)
  • Author(s): 福島孝治、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: 2011-03-25
• [Presentation] スピングラス模型における磁場下での非平衡関係式 (2011)
  • Author(s): 勝田仁之、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: 2011-03-25
• [Presentation] 磁気記録媒体の高密度集積化に現れる得意な現象 (2011)
  • Author(s): 大関真之、田中利幸
  • Organizer: 京都大学ICTイノベーション2011情報学シンポジウム
  • Place of Presentation: 京都大学
  • Year and Date: 2011-02-18
• [Presentation] Jarzynski equality for an energy-controlled system (2011)
  • Author(s): 勝田仁之、大関真之
  • Organizer: The third international workshop on Dynamics and Manipulation of Quantum Systems
  • Place of Presentation: 東京大学
  • Year and Date: 2011-02-15
• [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 in quantum annealing (2011)
  • Author(s): 大関真之、西森秀稔
  • Organizer: The third international workshop on Dynamics and Manipulation of Quantum Systems
  • Place of Presentation: 東京大学
  • Year and Date: 2011-02-14
• [Presentation] Jarzynski equality for an energy-controlled system (2011)
  • Author(s): 勝田仁之、大関真之
  • Organizer: International Symposium "Nanoscience and Quantum Physics 2011"
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-01-27
• [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
• [Presentation] Nonequilibrium work distribution in quantum annealing (2011)
  • Author(s): 大関真之、西森秀稔
  • Organizer: International Symposium "Nanoscience and Quantum Physics 2011"
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-01-26
• [Presentation] 双対変換から見るランダムネスの有意性 (2010)
  • Author(s): 大関真之, H.G.Katzgraber, H.Bombin, M.A.Martin-Delgado
  • Organizer: 日本物理学会第65回年次大会
  • Place of Presentation: 岡山大学, 日本
  • Year and Date: 2010-03-23
• [Presentation] Duality analysis for spin glasses (2010)
  • Author(s): 大関真之
  • Organizer: Young Scientists Meeting on Statistical Physics and Information Processing, YSM-SPIP2009
  • Place of Presentation: 東京工業大学, 日本
  • Year and Date: 2010-03-02
• [Presentation] Quantum Annealing with Jarzynski equality (2009)
  • Author(s): 大関真之, 西森秀稔
  • Organizer: Conference on Computational Physics 2009, CCP2009
  • Place of Presentation: Kaohsiung, Taiwan
  • Year and Date: 2009-12-17
• [Presentation] Jarzynski 等式を利用した量子アニーリング (2009)
  • Author(s): 大関真之
  • Organizer: JST/CREST量子情報処理システムの実現を目指した新技術の創出領域ワークショップ
  • Place of Presentation: 熱海, 日本
  • Year and Date: 2009-12-08
• [Presentation] Scaling law of the residual energy in simulated annealing (2009)
  • Author(s): 保田恵一, 大関真之, 西森秀稔
  • Organizer: JST/CREST量子情報処理システムの実現を目指した新技術の創出領域ワークショップ
  • Place of Presentation: 熱海, 日本
  • Year and Date: 2009-12-07
• [Presentation] Quantum annealing with Jarzynski equality (2009)
  • Author(s): 大関真之, 西森秀稔
  • Organizer: The second international workshop on dynamics and manipulation of quantum system
  • Place of Presentation: 東京, 日本
  • Year and Date: 2009-10-14
• [Presentation] Scaling law of the residual energy in simulated annealing (2009)
  • Author(s): 保田恵一, 大関真之, 西森秀稔
  • Organizer: The second international workshop on dynamics and manipulation of quantum system
  • Place of Presentation: 東京, 日本
  • Year and Date: 2009-10-14
• [Presentation] 双対変換によるスピングラス相転移点の解析 (2009)
  • Author(s): 大関真之, 西森秀稔
  • Organizer: 日本物理学会2009年秋季大会
  • Place of Presentation: 熊本大学, 日本
  • Year and Date: 2009-09-27
• [Presentation] Efficient Quantum Annealing by the Jarzynski Equality (2009)
  • Author(s): 大関真之
  • Organizer: Frontiers in Nonequilibrium Physics
  • Place of Presentation: 京都大学, 日本
  • Year and Date: 2009-07-31
• [Presentation] Efficient Quantum Annealing by the Jarzynski Equality (2009)
  • Author(s): 大関真之
  • Organizer: Workshop on Quantum Foundations for Young Researchers-From Mathematical Physics to Experimental Physics
  • Place of Presentation: 東京工業大学, 日本
  • Year and Date: 2009-07-11
• [Presentation] 2次元q状態Pottsモデリレのボンド希釈の相転移 (2009)
  • Author(s): 小村幸浩、岡部豊、大関真之
  • Organizer: 日本物理学会第64回年次大会
  • Place of Presentation: 立教大学
• [Presentation] Nonequilibrium Relations on Nishimori Line (2009)
  • Author(s): 大関真之, 西森秀稔
  • Organizer: International Symposium on Nanoscience and Quantum Physics nanoPHYS'09
  • Place of Presentation: 六本木・国際文化会館
• [Presentation] Zero-Temperature Complex Replica Zeros of ±J Ising Spin Glass on Mcan-filed systems and Beyond (2009)
  • Author(s): 小渕智之, 樺島祥之, 西森秀稔, 大関真之
  • Organizer: International Symposium on Nanoscience and Quantum Physics nanoPHYS'09
  • Place of Presentation: 六本木・国際文化会館
• [Presentation] Improved conjecture on the multicritical point of spin glass (2008)
  • Author(s): 大関真之
  • Organizer: Multicritical Behavior of Spin Glasses and Quantum Error Correcting Codes
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-11-18
• [Presentation] Improved conjecture on the multicritical point of spin glass (2008)
  • Author(s): 大関真之
  • Organizer: Multicritical Behaviour of Spin Glasses and Quan turn Error Correcting Codes (MBQEC)
  • Place of Presentation: 東京工業大学
• [Presentation] 双対変換によるランダム系の相境界 (2008)
  • Author(s): 大関真之, 西森秀稔
  • Organizer: 日本物理学会2008年秋季大会
  • Place of Presentation: 岩手大学
• [Presentation] Duality for Precise Locations of Critical Points in Random Spin Systems (2008)
  • Author(s): 大関真之
  • Organizer: JST/CREST第4回量子情報未来テーマ開拓研究会
  • Place of Presentation: 沖縄知念サンライズ
• [Book] 量子アニーリング、日本物理学会誌 (2011)
  • Author(s): 大関真之、西森秀稔
• [Book] 日本物理学会誌 66 (2011)
  • Author(s): 大関真之、西森秀稔
  • Publisher: 量子アニーリング
• [Book] スピングラス模型の臨界点と双対変換～厳密解を求めて～、物性研究 (2010)
  • Author(s): 大関真之
• [Book] 物性研究 94(4) (2010)
  • Author(s): 大関真之
  • 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～
• [Remarks] 受賞(1)大関真之日本物理学会若手奨励賞(領域11)、日本物理学会
• [Remarks] (2)大関真之JPSJ Papers of Editor's choice "Nonequilibrium Relations for Spin Glasses with Gauge Symmetry"、日本物理学会
• [Remarks] (3)大関真之、平成21年度手島精一記念研究賞博文論文賞、東京工業大学
• [Remarks] 新聞報道大関真之科学新聞2010年9月17日号.「スピングラスとジャルジンスキー等式-京大・東工大グループ厳密な関係式解明」
• [Remarks]
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