Equivalence and inequivalence of microcanonical and canonical ensembles in spin glasses

• Project/Area Number: 23540440
• 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: Tokyo Institute of Technology
• Principal Investigator: NISHIMORI Hidetoshi 東京工業大学, 理工学研究科, 教授 (70172715)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: ミクロカノニカル分布 / カノニカル分布 / スピングラス / 長距離相互作用 / カノニカルアンサンブル / 長距離相互作用系 / イジング模型 / アンサンブルの等価性 / アンサンブルの非等価性 / ランダム系 / スピン系

Outline of Final Research Achievements

Statistical mechanics aims to clarify the behavior of systems with many microscopic components. Microcanonical and canonical ensembles of statistical mechanics lead to the same results in most cases, but this is known not to be the case where the system has singular properties such as long-range interactions. In the present study, we have analytically clarified conditions under which the ensembles become equivalent or the mean-field theory gives exact answers.

Research Products

• [Journal Article] Mean-field theory is exact for the random-field model with long-range interactions (2014)
  • Author(s): Junichi Tsuda and Hidetoshi Nishimori
  • Journal Title: Journal of the Physical Society of Japan Volume: 83 Issue: 7 Pages: 074002-074002
  • DOI: 10.7566/jpsj.83.074002
  • NAID: 40020124484
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions (2012)
  • Author(s): Yuma Murata and Hidetoshi Nishimori
  • Journal Title: Journal of the Physical Society of Japan Volume: 81 Issue: 11 Pages: 1140081-7
  • DOI: 10.1143/jpsj.81.114008
  • NAID: 40019484124
  • Peer Reviewed
• [Journal Article] Ensemble equivalence in spin systems with short-range interactions (2011)
  • Author(s): Kazutaka Takahasi, Hidetoshi Nishimori and Victor Martin-Mayor
  • Journal Title: Journal of Statistical Mechanics Volume: -- Issue: 08 Pages: P08024-P08024
  • DOI: 10.1088/1742-5468/2011/08/p08024
  • Peer Reviewed
• [Journal Article] Ensemble inequivalence in the ferromagnetic p-spin model in random fields (2011)
  • Author(s): Z. Bertalan, T. Kuma, Y. Matsuda and H. Nishimori
  • Journal Title: Journal of Statistical Mechanics Volume: -- Issue: 01 Pages: P01016-P01016
  • DOI: 10.1088/1742-5468/2011/01/p01016
• [Presentation] Equivalence and inequivalence of canonical and microcanonical ensembles (2011)
  • Author(s): Hidetoshi Nishimori
  • Organizer: 中国物理学会(招待講演)
  • Place of Presentation: 中国 杭州
• [Presentation] Ensemble inequivalence in disordered spin systems (2011)
  • Author(s): Hidetoshi Nishimori
  • Organizer: Unifying concepts in glass physics V(招待講演)
  • Place of Presentation: フランス パリ
• [Remarks] 西森秀稔のウェブページ
  • URL: http://www.stat.phys.titech.ac.jp/~nishimori/