1999年海涅曼奖演讲:统计力学中的可积模型:具有未解决问题的隐藏领域
The 1999 Heineman Prize Address- Integrable models in statistical mechanics: The hidden field with unsolved problems
摘要:
在过去的30年里,在可积统计力学模型理论方面有了广泛的发现,包括伊辛模型关联函数的非线性微分方程的发现、随机杂质理论、手征Potts模型中的能级交叉跃迁以及Rogers-Ramanujan恒等式推广我们的玻色/费米统计概念。每一个这些进展导致进一步发现重大未解决的问题,极大的数学和物理利益。我将在这里讨论数学的进步,物理的见解和非凡的缺乏可见性的物理学这一领域。
英文摘要:
In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random impurities, level crossing transitions in the chiral Potts model and the use of Rogers-Ramanujan identities to generalize our concepts of Bose/Fermi statistics. Each of these advances has led to the further discovery of major unsolved problems of great mathematical and physical interest. I will here discuss the mathematical advances, the physical insights and extraordinary lack of visibility of this field of physics.
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