Lattice Gauge Theory of Three Dimensional Thirring Model

Abstract

Three dimensional Thirring model with $N$ four-component Dirac fermions, reformulated as a lattice gauge theory, is studied by computer simulation. According to an $8^{3}$ data and preliminary $16^3$ data, chiral symmetry is found to be spontaneously broken for $N=2,\;4$ and 6. $N=2$ data exhibits long tail of the non-vanishing chiral condensate into weak coupling region, and $N=6$ case shows phase separation between the strong coupling region and the weak coupling region. Although the comparison between $8^3$ data and $16^3$ data shows large finite volume effects, an existence of the critical fermion flavor number $N_{\rm cr}$ $(2<N_{\rm cr}<6)$ for which the chiral behavior changes its character, is suggested by the current numerical data.