3D XY scaling theory of the superconducting phase transition

The intermediate 3D XY scaling theory of superconductivity at zero and nonzero magnetic fields is developed, based only upon the dimensional hypothesis $B\sim (Length)^{-2}$. Universal as well as nonuniversal aspects of the theory are identified, including background terms and demagnetization effects. Two scaling regions are predicted: an "inner" region (very near the zero field superconducting transition, $T_c$), where the fields $B$, $H$, and $H_{ex}$ differ substantially, due to the presence of diamagnetic fluctuations, and an "outer" region (away from $T_c$), where the fields can all be treated similarly. The characteristic field ($H_0$) and temperature ($t_1$) scales, separating the two regimes, are estimated. Scaling theories of the phase transition line, magnetization, specific heat, and conductivity are discussed. Multicritical behavior, involving critical glass fluctuations, is investigated along the transition line, $T_m(B)$, at nonzero fields.

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