Information Theory for Spin Glasses

In this study, we focus on the fact that the equilibrium state of a magnetic material, called spin glass, can be described as a solution to the system of equations that defines lossy compression of information. We used the analytical expression of the rate-distortion function which describes the best performance for lossy compression, so that we can theoretically evaluate the critical properties of spin glass without worrying about numerical issues. This scenario is interesting from the point of view of basic research, since it tries to reverse the methodological direction of the trend in applied physics, where concepts and methods of statistical physics have been applied to problems in information science. As a result, a classical theorem in information theory, which has been expected to be powerful in rigorous evaluations, proved to be useful as a toolbox for analyzing spin glass models as well.

本研究は、統計物理学の概念と方法を情報科学の諸課題に応用していく従来の研究志向を逆転させているのが学術的な特色である。この新しいパラダイムの提唱によって、統計物理学の適用範囲が事実上拡大し、未知の現象の発見及びその理論的説明ができるようになる。特に、その複雑さゆえ、現在は数値解析が主流となっているスピングラスの研究に再び革新をもたらす可能性がある。また同時に、情報理論の新しい適用先が開拓できたという学術的意義も大きい。