Tricritical Ratio of Length Scales in theD=4Abelian Higgs Model

We use the duality between the Abelian Higgs model and pure U(1) lattice gauge theory to estimate the ratio $\sqrt{2}\kappa =\frac{\lambda }{\xi }$ of penetration depth and coherence length at the tricritical point to be $\sqrt{2}\kappa \approx 0.93$, thus placing the tricritical point slightly on the type-I side of the borderline between type-I and type-II superconductivity in four dimensions.