Loop representation for 2-D Wilson lattice fermions in a scalar background field

Abstract

We show that the fermion determinant for 2-D Wilson lattice fermions coupled to an external scalar field is equivalent to self avoiding loops interacting with the external field. In an application of the resulting formula we integrate the scalar field with a Gaussian action to generate the N-component Gross-Neveu model. The loop representation for this model is discussed.

References in corpus (2)

• A formula for the hopping expansion of 8-vertex models coupled to an external field
• Hopping expansion as a tool for handling dual variables in lattice models

Cited by in corpus (14)

• Approaches to the sign problem in lattice field theory
• Solving the sign problems of the massless lattice Schwinger model with a dual formulation
• Efficient simulation of relativistic fermions via vertex models
• Cluster simulation of relativistic fermions in two space-time dimensions
• Simulating the All-Order Hopping Expansion II: Wilson Fermions
• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• The lattice Schwinger model as a discrete sum of filled Wilson loops
• Fermion loop simulation of the lattice Gross-Neveu model
• Anomalous discrete chiral symmetry in the Gross-Neveu model and loop gas simulations
• A formula for the hopping expansion of 8-vertex models coupled to an external field
• Unexpected Results in the Chiral Limit with Staggered Fermions
• Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential
• Isocliny in spinor space and Wilson fermions
• Fermion loop simulations in 2--d lattice theories -- results and limitations