Analytic vortex solutions in an unusual Mexican hat potential

TL;DR

This paper introduces a novel piecewise parabolic Mexican hat potential and derives its vortex solutions analytically, providing a new approach compared to traditional Psi^4 field theory.

Contribution

It presents an analytical method for vortex solutions in a new Mexican hat potential, differing from standard models.

Findings

Vortex solutions are obtained analytically for the new potential.

The potential is piecewise parabolic, unlike the standard form.

Analytical solutions contrast with numerical methods used previously.

Abstract

We introduce an unusual Mexican hat potential, a piecewise parabolic one, and we show that its vortex solutions can be found analytically, in contrast to the case of the standard Psi^4 field theory.