<p>We propose a novel method to distinguish states of matter by identifying spontaneous symmetry breaking on extended objects, such as vortices, even in the absence of a bulk phase transition. As a specific example, we investigate the phase transition on superfluid vortices in the Higgs-confinement crossover using a U(1)_gauge × U(1)_global model in (3 + 1) dimensions. This model exhibits superfluidity of U(1)_global symmetry and allows for a crossover between the Higgs and confinement regimes by varying the gauge coupling constant from weak to strong. We demonstrate that, on vortices, spontaneous breaking of the ℤ₂ flavor symmetry occurs in the weak coupling (Higgs) regime, while it does not in the strong coupling (confinement) regime. We also confirm that those regimes are separated by a second-order phase transition through Monte Carlo simulations, whose universality class corresponds to the two-dimensional Ising model.</p>