Statistical mechanics is one of the main research directions of Yang Zhenning. His characteristic in statistical mechanics is to strictly solve and analyze the general model rooted in physical reality, so as to grasp the essence and essence of the problem.
From 65438 to 0952, Yang Zhenning and his collaborators published three important papers on phase transition. The first paper is about the spontaneous magnetization of two-dimensional Ising model, which he independently completed the year before last, and obtained the critical exponent of 1/8. This is the longest calculation that Yang Zhenning has ever done. Ising model is the most basic but extremely important model in statistical mechanics, but its importance in theoretical physics was not widely recognized until 1960s.
1952, Yang Zhenning also cooperated with Li Zhengdao to complete and publish two papers on phase transition theory. Two articles were submitted and published at the same time, which aroused Einstein's interest. In this paper, the analytic properties of giant partition function are studied by analytic continuation method, and it is found that the distribution of its roots determines the state equation and phase transition properties, which eliminates the suspicion that different thermodynamic phases can exist under the same interaction.
The climax of these two papers is the unit circle theorem in the second paper, which points out that the zero point of the giant partition function of the lattice gas model attracting interaction lies on the unit circle on the complex plane.
2. Boson many-body problem
Out of his interest in liquid helium superfluid, Yang Zhenning published or completed a series of papers on thin boson multibody systems with his collaborators around 1957.
First, he published two papers with Huang and Luttinger, and applied the pseudopotential method to this field. After writing the article "Is parity conserved in weak interaction", while waiting for the experimental results, the correct ground state energy correction was obtained by the double collision method, and then the same results were obtained by the pseudo-potential method.
The most surprising energy correction they got was the famous square root correction term, but it could not be verified by experiments at that time. However, with the development of cold atomic physics, this correction term has been confirmed by experiments.
3. Young-Baxter equation
In 1960s, Yang Zhenning found the strict solution of quantum statistical model by trying to find off-diagonal long program model. 1967, it was found that the fermion quantum many-body problem in the repulsive potential of 1 dimensional δ function could be transformed into a matrix equation, which was later called Yang-Baxter equation (because Baxter also found this equation in another problem of 1972).
In 1967, Yang Zhenning also wrote an article published in the following year, which further discussed the problem of S matrix. Later, it was found that Yang -—Baxter equation is an extremely important equation in mathematics and physics, which is closely related to kink theory, braid group, Hopf algebra and even string theory.
The 1 dimensional fermion problem discussed by Yang Zhenning is very important in the experimental study of cold atoms. The nested Bethe hypothesis method he invented in this paper was used by Lieb and Wu Fayue to solve the 1 dimensional Hubbard model the following year. Hubbard model later became the basis of many theoretical studies on high temperature superconductivity.
4. Theoretical explanation of superconducting magnetic ionization.
196 1 year, through close communication with Fei Zhengqing experimental group, Yang Zhenning and byers theoretically explained the superconducting magnetic ionization discovered by the experimental group, proved that electron pairing can lead to observed phenomena, clarified the basic principle of electromagnetic field without introducing new principles, and corrected the mistakes of London reasoning.
In this work, Yang Zhenning and byers applied gauge transformation technique to condensed matter system. Related physics and methods were later widely used in the study of superconductivity, superfluidity and quantum Hall effect.
5. Off-diagonal long program
1962, Yang Zhenning put forward the concept of "long-range order from two angles", thus describing the essence of superfluidity and superconductivity in a unified way, and deeply discussing the root of flux ionization.
This is a key concept of contemporary condensed matter physics. From 1989 to 1990, Yang Zhenning found the eigenstate with off-diagonal long program in the Hubbard model closely related to HTS, and found its SO(4) symmetry with Zhang Shousheng.