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.
