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:
“Every woman who visited the Fair made it the center of her orbit. Here was a structure designed by a woman, decorated by women, managed by women, filled with the work of women. Thousands discovered women were not only doing something, but had been working seriously for many generations ... [ellipsis in source] Many of the exhibits were admirable, but if others failed to satisfy experts, what of it?”
—Kate Field (1838–1908)
“... the first reason for psychology’s failure to understand what people are and how they act, is that clinicians and psychiatrists, who are generally the theoreticians on these matters, have essentially made up myths without any evidence to support them; the second reason for psychology’s failure is that personality theory has looked for inner traits when it should have been looking for social context.”
—Naomi Weisstein (b. 1939)