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This is because Landau theory is a mean field theory, and does not include long-range correlations. This theory does not explain non-analyticity at the critical point, but when applied to superfluid and superconductor phase transition, Landau's theory provided inspiration for another theory, the Ginzburg–Landau theory of superconductivity.
In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic that are free to vary).
One of the major discoveries in the study of critical phenomena is that mean field theory of critical points is only correct when the space dimension of the system is higher than a certain dimension called the upper critical dimension which excludes the physical dimensions 1, 2 or 3 in most cases. The problem with mean field theory is that the ...
In Landau mean-field theory, at temperatures near the superconducting critical temperature , () (/). Up to a factor of 2 {\displaystyle {\sqrt {2}}} , it is equivalent to the characteristic exponent describing a recovery of the order parameter away from a perturbation in the theory of the second order phase transitions.
Using this in the Landau theory, which is identical to the mean field theory for the Ising model, the value of the upper critical dimension comes out to be 4. If the dimension of the space is greater than 4, the mean-field results are good and self-consistent. But for dimensions less than 4, the predictions are less accurate.
Based on Landau's previously established theory of second-order phase transitions, Ginzburg and Landau argued that the free energy density of a superconductor near the superconducting transition can be expressed in terms of a complex order parameter field () = | | (), where the quantity | | is a measure of the local density of superconducting electrons () analogous to a quantum mechanical wave ...
In the second edition, the corresponding sections were scrapped and replaced with more topics in the well-established quantum electrodynamics, and the two parts were unified into one, thus providing a one-volume exposition on relativistic quantum field theory with the electromagnetic interaction as the prototype of a quantum field theory.
Robert T. Craig "Communication Theory as a Field" is a 1999 article by Robert T. Craig, attempting to unify the academic field of communication theory. [1] [2]Craig argues that communication theorists can become unified in dialogue by charting what he calls the "dialogical dialectical tension", or the similarities and differences in their understanding of "communication" and demonstrating how ...