# The order of the phase transition in 3d U(1)+Higgs theory

## TL;DR

This paper investigates the nature of the phase transition in 3d U(1)+Higgs theory, revealing that the order changes from first to possibly higher than second as scalar self-coupling increases.

## Contribution

It provides evidence that the phase transition's order depends on scalar self-coupling, with a transition from first order to higher order regimes.

## Key findings

- First order transition at small scalar self-coupling.
- Transition may become higher than second order at large scalar self-coupling.
- Scalar mass remains non-zero near the transition.

## Abstract

We study the order of the phase transition in the 3d U(1)+Higgs theory, which is the Ginzburg-Landau theory of superconductivity. We confirm that for small scalar self-coupling the transition is of first order. For large scalar self-coupling the transition ceases to be of first order, and a non-vanishing scalar mass suggests that the transition may even be of higher than second order.