Gross -neveau model on lattice

Abstract

This is a report on the analytical study of the Gross-Neveu model and its simulation on a discrete space-time lattice. Firstly, the symmetries of the Gross-Neveu Lagrangian will be studied. Next, the spontaneous breaking of chiral symmetry of the model will be demonstrated . Then, it will be shown that the theory described by the model is asymptotically free. In lattice, the path integral quantization of the model Lagrangian is carried out by the Hybrid Monte Carlo (HMC) algorithm is used. To integrate the Hamilton’s equations of motion of the fields and their conjugate momenta, various integrators such as leap-frog, Omelyan and the Force-Gradient integrators will be used. Their performance in generating uncorrelated configurations will be studied.