Efficient simulation of relativistic fermions via vertex models

We have developed an efficient simulation algorithm for strongly interacting relativistic fermions in two-dimensional field theories based on a formulation as a loop gas. It essentially eliminates critical slowing down by sampling two-point correlation functions and allows simulations directly in the massless limit at the critical point. It generates loop configurations with fluctuating topological boundary conditions enabling one to simulate fermions with arbitrary periodic or antiperiodic boundary conditions. As illustrative examples, the algorithm is applied to the Gross-Neveu model and to the Schwinger model in the strong coupling limit.