The exact equivalence of the one-flavour lattice Thirring model with Wilson fermions to a two-colour loop model

Abstract

Within Euclidean lattice field theory an exact equivalence between the one-flavour 2D Thirring model with Wilson fermions and Wilson parameter $r=1$ to a two-colour loop model on the square lattice is established. For non-interacting fermions this model reduces to an exactly solved loop model which is known to be a free fermion model. The two-colour loop model equivalent to the Thirring model can also be understood as a 4-state 49-vertex model.

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References in corpus (6)

• Cluster Algorithm for Vertex Models
• Four - Fermi Theories in Fewer Than Four Dimensions
• Solvable lattice models labelled by Dynkin diagrams
• The exact equivalence of the two-flavour strong coupling lattice Schwinger model with Wilson fermions to a vertex model
• Four State Models and Clifford Algebras
• The L-Matrix for the Massive Thirring Model

Cited by in corpus (6)

• Efficient simulation of relativistic fermions via vertex models
• Simulating the All-Order Hopping Expansion II: Wilson Fermions
• 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
• A formula for the hopping expansion of 8-vertex models coupled to an external field
• Isocliny in spinor space and Wilson fermions