The Map Drawn by a Fitted Pair: Ginzburg and Landau's Functional and the Price of Its Coefficients
Year: 2026
Type: preprint
Abstract: In 1950 Ginzburg and Landau gave superconductivity its order parameter: a complex field \psi with a free energy of Landau's analytic form plus a gauge-coupled gradient term. From that functional flow the coherence length, the penetration depth, their ratio \kappa, and the type-I/type-II divide at \kappa = 2^{-1/2} that still organizes the superconducting world. The functional's two coefficients, \alpha(T) and \beta, are phenomenological inputs, and \alpha's sign change at T_c is stipulated to be linear. This paper audits the fitting. On declared tabulated (\xi, \lambda) pairs the bench returns \kappa for five named superconductors (0.031250 to 1.026316 against the divide 0.707107), computes how far each fitted input must move, alone, to flip its material's class (+58.621251\% of \lambda for lead; -31.102416\% for niobium), and returns the coherence length's divergence under the stipulated linear \alpha(T) against a quadratic alternative: the famous exponent 0.500000 is the stipulation's exponent halved. The map is the fitted pair's placement; the exponent is the stipulation read back. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.
Author: Aldred, William Alexander
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225417184