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

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.

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References in corpus (5)

• Solvable lattice models labelled by Dynkin diagrams
• Strong Coupling Lattice Schwinger Model on Large Spherelike Lattices
• Lee-Yang zeroes in the one flavour massive lattice Schwinger model
• Exact solution (by algebraic methods) of the lattice Schwinger model in the strong-coupling regime
• Exact solution of new integrable nineteen-vertex models and quantum spin-1 chains

Cited by in corpus (6)

• Efficient simulation of relativistic fermions via vertex models
• The lattice Schwinger model as a discrete sum of filled Wilson loops
• Loop representation for 2-D Wilson lattice fermions in a scalar background field
• The exact equivalence of the one-flavour lattice Thirring model with Wilson fermions to a two-colour loop model
• Some approximate analytical methods in the study of the self-avoiding loop model with variable bending rigidity and the critical behaviour of the strong coupling lattice Schwinger model with Wilson fermions
• Isocliny in spinor space and Wilson fermions