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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 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.
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The classical Landau theory (also known as mean field theory) values of the critical exponents for a scalar field (of which the Ising model is the prototypical example) are given by = ′ =, =, = ′ =, =
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). Such models ...
The series presently stands at four books (as of early 2023) covering the first four of six core courses devoted to: classical mechanics, quantum mechanics, special relativity and classical field theory, general relativity, cosmology, and statistical mechanics. Videos for all of these courses are available online.
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 ...
The Ginzburg–Landau equation is the governing equation for . The unstable modes can either be non-oscillatory (stationary) or oscillatory. [1] [2] For non-oscillatory bifurcation, satisfies the real Ginzburg–Landau equation