A cluster algorithm for Gross-Neveu fermions at nonzero temperature

Abstract

In this thesis we present results of lattice simulations of Gross-Neveu fermions in 1+1 dimensions. We re derive the representation of N flavors of Wilson fermions in terms of Ising spins on a 1 + 1 dimensional lattice from [1]. We re implement the cluster algorithm of [1] for N flavors of free fermions and verify it against exact monomer densities in the free theory. In addition, we extend this algorithm to the interacting case using the prescription outlined in [1] and produce results for fermion correlation functions in the Gross-Neveu model using a cluster algorithm for the first time. To analyze Gross-Neveu fermions at nonzero temperature, we develop an algorithm to simulate fluctuating boundary conditions. We calculate the chiral condensate at nonzero temperature using this algorithm and see evidence consistent with a phase transition in the large N limit.