- Broida 1640
Leo P. Kadanoff - University of Chicago/The Perimeter Institute
This talk describes how physicists and chemists mostly ignored basic mathematics in constructing theories of phase transitions: It details the prices they paid for this insolence, and the gains it permitted.
In present-day physics, the renormalization method, as developed by Kenneth G. Wilson, serves as the primary means for constructing the connections between theories at different length scales. This method is rooted in both particle physics and the theory of phase transitions. Renormalization methods were developed to supplement mean field theories like those developed by van der Waals and Maxwell, followed by Landau.
Sharp phase transitions are necessarily connected with singularities in statistical mechanics, which in turn require infinite systems for their realization. The argument then suggests that phase transitions should be described by connecting microscopic symmetry-breaking with macroscopic constraints applied at the far boundaries of the system.
Mean field theories neither demand nor employ spatial infinities in their descriptions of phase transitions. Another theory is required that weds a breaking of internal symmetries with a proper description of spatial infinities. The renormalization (semi-) group provides such a wedding. Its nature is described.