In this thesis, we study the N = 2 chiral Ising Gross-Neveu universality class. Gross-Neveu universality classes describe the transitions of relativistic Dirac fermions to insulators or condensed states. These strongly correlating fermion systems are not only interesting to particle physics but also appear in a wide range of condensed matter systems. Here, we develop a model that satisfies the conditions for a Majorana positive decomposition, enabling the possible first sign-problem free quantum Monte Carlo simulation of the desired class. The resulting system exists on the 2D bilayer square lattice, with anisotropic long-range hopping and without Berry flux. The long-range hopping dominates along the major axes, similar to SLAC fermions. The work involves the use of projector quantum Monte Carlo simulation to study the developed model at half-filling. We extract the critical exponents and compare them to the known results for the class, which provides confidence in our model and offers new insights into the universality class.