Chiral critical behavior of 3D lattice fermionic models with quartic interactions

We study the critical behavior of three-dimensional Gross-Neveu (GN) model with ${N}_{f}$ four-component Dirac fermionic flavors and quartic interactions, at chiral ${\mathbb{Z}}_{2}$ transition in massless ${\mathbb{Z}}_{2}$-symmetric limit. For this purpose, we consider a lattice GN staggered Kogut-Susskind fermions scalar field coupled to bilinear operator, which effectively realizes attractive four-fermion interaction. perform Monte Carlo simulations for ${N}_{f}=4$, 8, 12, 16. By means finite-size scaling analyses numerical data, obtain estimates exponents, are compared large-${N}_{f}$ predictions obtained using continuum theory. observe substantial agreement. This confirms that models provide nonperturbative realization quantum theory, even though interactions explicitly break flavor $\mathrm{U}({N}_{f})\ensuremath{\bigotimes}\mathrm{U}({N}_{f})$ symmetry is only recovered