Yang has had a great interest in statistical mechanics since his undergraduate time. In the 1950s and 1960s, he collaborated with Tsung Dao (T.D.) Lee and Kerson Huang, etc. and studied statistical mechanics and condensed matter theory. He studied the theory of phase transition and elucidated the Lee–Yang circle theorem, properties of quantum boson liquid, two dimensional Ising model, flux quantization in superconductors (with N. Byers, 1961), and proposed the concept of Off-Diagonal Long-Range Order (ODLRO, 1962). In 1967, he found a consistent condition for a one dimensional factorized scattering many body system, the equation was later named the Yang–Baxter equation, it plays an important role in integrable models and has influenced several branches of physics and mathematics.