2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/39145In World Line Path Integral representation Abelian Higgs theories admit a curvature term in the Hamiltonian. Using Monte Carlo simulations we show that the curvature term drives a phase transition at sufficiently strong coupling. In quenched approximation this phase transition is smooth, with implications that the model reduces to a Goldstone theory. Critical properties of the system near the transition are investigated and found to be consistent with mean field behavior.14 pages with 6 figuresHigh Energy Physics - Latticetext