A Phase Transition in U(1) Configuration Space: Oscillons as Remnants of Vortex-Antivortex Annihilation

Abstract

We show that the low-momentum scattering of vortex-antivortex pairs can lead to very long-lived oscillon states in 2d Abelian Higgs models. The emergence of oscillons is controlled by the ratio of scalar and vector field masses, $\beta=(m_s/m_v)^2$ and can be described as a phase transition in field configuration space with critical value $\beta_c\simeq 0.13(6)\pm 2 $: only models with $\beta<\beta_c$ lead to oscillon-like remnants. The critical behavior of the system obeys a power law $O(\beta)\sim |\beta-\beta_c|^o$, where $O$ is an order parameter indicating the presence of oscillons and $o = 0.2(2)\pm 2 $ is the critical exponent.