# Topological transitions in the euclidean 2d U(1)-Higgs model

## TL;DR

This paper investigates topological transitions in the 2D Euclidean U(1)-Higgs model, analyzing sphaleron transition rates through lattice simulations and their relation to vortex formation and Chern-Simons number behavior.

## Contribution

It provides a novel analysis of sphaleron transitions in the 2D Euclidean U(1)-Higgs model using lattice simulations at finite temperature.

## Key findings

- Sphaleron transition rates can be inferred from vortex formation.
- Chern-Simons number behavior correlates with topological transitions.
- High-temperature Euclidean simulations reveal insights into topological dynamics.

## Abstract

The two-dimensional U(1)-gauged Higgs model is studied on an euclidean lattice of size $L_1\times L_2$, where the temperature $T=L_2^{-1}$ is of the order of the sphaleron mass. The simulation parameters are taken from zero temperature results. By comparison with classical and semiclassical results I discuss, whether the sphaleron transition rate can be extracted from the behavior of the Chern-Simons number and from the formation of vortices in an euclidean simulation at high temperatures.