# The exact equivalence of the two-flavour strong coupling lattice Schwinger model with Wilson fermions to a vertex model

## TL;DR

This paper demonstrates an exact equivalence between the two-flavour strong coupling lattice Schwinger model with Wilson fermions and a modified 3-state 20-vertex model, extending previous work on the one-flavour case.

## Contribution

It applies a known method to establish an exact vertex model representation for the two-flavour case, broadening the understanding of lattice gauge theories with Wilson fermions.

## Key findings

- Identifies a 20-vertex model equivalent to the two-flavour Schwinger model
- Shows the vertex model can be viewed as a loop model
- Extends the method to models with multiple flavours and dimensions

## Abstract

In this paper a method previously employed by Salmhofer to establish an exact equivalence of the one-flavour strong coupling lattice Schwinger model with Wilson fermions to some 8-vertex model is applied to the case with two flavours. As this method is fairly general and can be applied to strong coupling QED and purely fermionic models with any (sufficiently small) number of Wilson fermions in any dimension the purpose of the present study is mainly a methodical one in order to gain some further experience with it. In the paper the vertex model equivalent to the two-flavour strong coupling lattice Schwinger model with Wilson fermions is found. It turns out to be some modified 3-state 20-vertex model on the square lattice, which can also be understood as a regular 6-state vertex model. In analogy with the one- flavour case, this model can be viewed as some loop model.