Japan Long Term Visit: Study of Exactly Solvable Models in Statistical Mechanics

该奖项将资助俄克拉荷马州立大学物理系Jacques H.H.Perk教授和Helen Au-Yang教授长期访问日本，与位于日本京都大学的数学科学研究所(RIMS)的Mibo Michio Jimbo、Tetsuji Miwa和Mikio Sato教授共同开展一个研究项目。他们的研究将包括继续研究手征Potts模型中恒星-三角形(Yang-Baxter)方程的新的高亏格解。他们还将继续研究不规则晶格上Z不变非均匀伊辛模型的自旋-自旋关联函数。这些结果可以提供某些准晶和某些准周期伊辛晶格的关联函数。这一研究在统计力学、低维量子场论和完全可积系统中都具有重要意义。更高亏格解的进展可能会在数学和物理的许多其他研究领域之间产生相互作用。RIMS是国际和平研究所开展研究的理想机构。日本研究人员在世界上任何机构的可积系统方面拥有最大的集体知识和专业知识。帕克教授和欧阳教授是美国为数不多的研究可解模型的最好的研究人员之一。两国的研究人员在各自的领域都非常知名和受人尊敬。预计，在该奖项到期后，研究人员之间的合作可能会继续下去。

This award will support a long-term visit by Professors Jacques H.H. Perk and Helen Au-Yang, Department of Physics, Oklahoma State University to travel to Japan to undertake a joint research project with Professors Michio Jimbo, Tetsuji Miwa and Mikio Sato who are located at the Research Institute for Mathematical Sciences (RIMS) which is located at Kyoto University in Japan. Their research will involve continuous studies of the new higher-genus solutions of the star- triangle (Yang-Baxter) equation in the chiral Potts model. They will also continue research on the spin-spin correlation functions of the Z-invariant inhomogeneous Ising model on an irregular lattice. The results may provide correlation functions of certain quasicrystals and of some quasiperiodic Ising lattices. This research is of fundamental importance in statistical mechanics, in low-dimensional quantum field theory and completely integrable systems. Progress on the higher-genus solutions may bring forth interaction between many other research areas in mathematics and physics. RIMS is the ideal Institute for the PI's to carry out their research. The Japanese researchers have the greatest collective knowledge and expertise of integrable systems of any institution in the world. Professors Perk and Au-Yang are among the few best researchers in solvable models in the U.S. The researchers from both countries are all very well known and respected in their field. It is expected that, following the expiration of this award, collaborations between the researchers are likely to continue.