The φ 4 and the Gross-Neveu-Yukawa models have shown to be of great importance in physics. Even though the φ 4 model happens to be the most simple interacting quantum field theory, it has proven to be a reference point for the study of spontaneous symmetry breaking and renormalization [21] [23]. Its great importance lies, among other examples, in that it turns out to be intimately related to the description of the Higgs field in the standard model [15], and in the fact that it presents a universality class correspondence with the Ising Model [13]. The Gross-Neveu-Yukawa model is a a quartic interaction fermionic field theory, whose importance resides in the fact that it plays a strong role as toy model for Quantum Chromodynamics [11], it shows dynamical symmetry breaking, it has a spectrum of bound states and it is asymptotically free [7]. The Gross Neveu model with two flavors of Majorana fermions is equivalent to the Thirring model [29].
Lattice simulations of this models have been performed in the past (e.g. [13], [24]) using Markov Chain Monte Carlo method (specially making extensive use of the Metropolis-Hasting Algorithm). A further improvement over Metropolis-Hasting called Hamiltonian Monte Carlo has also been put in practice (see e.g. [17]). The HMC algorithm has the feature of combining global moves with high acceptance rates, improving in this way the quality of the produced statistics and the reduction of autocorrelation lengths [8] [22] 4.
Here we developed a software that applies Hamiltonian Monte Carlo and Wilson Fermions (a technique used to dynamically sample the fermion fields [31] [10]) for the generation of Markov Chain series for the φ 4 and GNY models in three dimensions and two fermionic flavors, ready for their use in statistical computation of observables and order parameters of these theories for critical phenomena study. Here HPC comes into play because this type of simulations introduces the challenge of dealing with massive linear algebra operations in which the memory and computational bounds are easily reached