Application of the maximum entropy method to the(2+1)Dfour-fermion model

We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the $\mathrm{}(2+1)\mathrm{}$-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the $\pi$ and permit an estimate of the meson binding energy. We have, however, seen no signal of $\overrightarrow{\sigma }\pi \pi$ decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.