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

TL;DR

This paper demonstrates that in 2D Abelian Higgs models, vortex-antivortex annihilation can produce long-lived oscillon states, with their emergence governed by a phase transition depending on the mass ratio of scalar and vector fields.

Contribution

It identifies a phase transition controlling oscillon formation based on the mass ratio parameter, providing a quantitative critical exponent and behavior.

Findings

Oscillons form only when the mass ratio parameter is below a critical value.

The emergence of oscillons follows a power-law behavior near the critical point.

The critical exponent for the phase transition is approximately 0.2.

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.