This award supports collaborative work in condensed matter physics between Dr. F. Y. Wu, Northeastern University, and Dr. Keh-Ying Lin of National Tsing Hua University, Taiwan. The objective of the research program is to obtain exact results in models of phase transitions and critical phenomena using rigorous mathematical analyses. Results of this research will enhance our understanding of the critical point phenomena such as freezing and provide guidance to other studies in condensed matter physics using numerical and approximation approaches.