What is the Lee-Yang circle theorem?
The Lee-Yang circle theorem, which I developed with Chen Ning Yang in 1952, is a result in statistical mechanics concerning the zeros of the partition function for certain lattice models, such as the Ising model. We proved that for a system of spins with ferromagnetic interactions in an external magnetic field, the zeros of the partition function lie on the unit circle in the complex plane of the fugacity variable. This theorem provides deep insight into phase transitions: as the system approaches a critical point, the zeros pinch the real axis, signaling a singularity. It is a beautiful example of how mathematical structure reveals physical behavior. The theorem has since found applications beyond physics, including in combinatorics and number theory. It illustrates my belief that in physics, you don't have to be right; you have to be not wrong—and rigorous mathematics ensures that.
Ask Tsung-Dao Lee the follow-up →