Mathematical Sciences: Studies of Exactly Solvable Models in Statistical Mechanics

点击翻译按钮获取中文摘要

9307816 Perk This is a research project for the continuation of the study of many of the unsolved problems in the chiral Potts model, generalized chiral Potts models, and multi-component chiral Potts models. These mathematical models describe phase transitions in experimentally realizable systems such as adsorption of molecules on thin films, multi-layered systems, membranes, etc. In spite of many successes so far in calculating various physical quantities of the chiral Potts model, these results have not yet been fully explored and made use of. It is intended in this project to translate the exact results into language more transparent to physicists, so that experts in Monte Carlo calculations, high- and low-temperature expansions, and various other methods, can use them. The exact results can be then used to properly gauge the errors of the approximate methods and solve long-standing controversies. Attempts to obtain new solvable models in three dimensions will be made in collaboration with our Russian colleague Yu.G. Stroganov. Progress in this work may bring forth interaction between many other research areas in mathematics and physics such as quantum groups and knot theory, monopoles and string theory, phase transitions in condensed matter, and biomembranes in biophysics. ! ! A ( Times New Roman Symbol & Arial " h ; % ; % / terri l. hicks terri l. hicks