Mean Field Theory
The classical Landau theory (aka mean field theory) values for a scalar field are
If we add derivative terms turning it into a mean field Ginzburg–Landau theory, we get
One of the major discoveries in the study of critical points is that mean field theory is completely wrong in the vicinity of critical points in two and three dimensions. In four dimensions, we have logarithmic corrections.
Read more about this topic: Critical Exponent
Famous quotes containing the words field and/or theory:
“Mine was, as it were, the connecting link between wild and cultivated fields; as some states are civilized, and others half-civilized, and others savage or barbarous, so my field was, though not in a bad sense, a half-cultivated field. They were beans cheerfully returning to their wild and primitive state that I cultivated, and my hoe played the Ranz des Vaches for them.”
—Henry David Thoreau (1817–1862)
“It is not enough for theory to describe and analyse, it must itself be an event in the universe it describes. In order to do this theory must partake of and become the acceleration of this logic. It must tear itself from all referents and take pride only in the future. Theory must operate on time at the cost of a deliberate distortion of present reality.”
—Jean Baudrillard (b. 1929)