  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. The loop models describing the dynamics of the fermions can be
mapped to statistical vertex models and our proposal is in fact an efficient
simulation algorithm for generic vertex models in arbitrary dimensions. The
algorithm essentially eliminates critical slowing down by sampling two-point
correlation functions and it allows simulations directly in the massless limit.
Moreover, it generates loop configurations with fluctuating topological
boundary conditions enabling to simulate fermions with arbitrary periodic or
anti-periodic boundary conditions. As illustrative examples, the algorithm is
applied to the Gross-Neveu model and to the Schwinger model in the strong
coupling limit.
