Monte Carlo simulations of systems with fermions

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Abstract
We present results of a Monte Carlo evaluation of the path integral for two-dimensional theories with fermions. These include fermions coupled to scalar fields and fermions coupled to Abelian gauge bosons. On a 10 by 10 lattice we have computed expectation values of local operators and correlation functions, from which we have estimated mass gaps. In the case of the coupled gauge-fermion system we find dynamical mass generation for both fermions and gauge bosons. We discuss the phase diagram and the continuum limit of the theory.