# Scaling in the two-dimensional U(1)--Higgs model

## TL;DR

This paper investigates the continuum limit of the 2D U(1)--Higgs model with variable scalar field length, confirming an instanton-induced confinement mechanism through numerical simulations of topological susceptibility.

## Contribution

It introduces the study of the 2D U(1)--Higgs model with variable scalar field length and demonstrates the instanton-induced confinement mechanism via numerical analysis.

## Key findings

- Confirmation of instanton-induced confinement
- Scaling behavior of topological susceptibility analyzed
- Difference from fixed length scalar field case

## Abstract

We study the continuum limit of the $2D$ U(1)--Higgs model with variable scalar field length, which is qualitatively different from the fixed length case. Our simulations concentrate on the scaling behaviour of the topological susceptibility, and an instanton-induced confinement mechanism of fractional charges is numerically confirmed.