Reply to comment on "Continuum dual theory of the transition in 3D lattice superconductor"

TL;DR

This paper clarifies that in 3D superconductors, the penetration depth and correlation length diverge with the same critical exponents, correcting previous faulty predictions based on improper dual theory treatment.

Contribution

It demonstrates that the critical behavior of the penetration depth and correlation length are identical, correcting earlier theoretical predictions by properly tuning the dual theory's coupling constants.

Findings

Penetration depth and correlation length diverge with same critical exponents.

Faulty previous predictions resulted from improper dual theory treatment.

Correct analysis aligns with general scaling arguments and independent calculations.

Abstract

It is argued that the penetration depth and the correlation length at the critical point of the 3D superconductor diverge with the same critical exponents, as follows from the general scaling arguments and from the independent calculations in both Ginzburg-Landau and its dual theory. The incorrect prediction of Kiometzis, Kleinert and Schakel (KKS) that this is is not so, is the result of the faulty treatment of the dual theory, in which two, instead of one, coupling constants are tuned to reach the critical point. The recent paper by the present author criticized by KKS in cond-mat/9702159 differs on this point from KKS, and consequently finds the expected relation between the divergence of the two lengths in the critical region.