Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models

TL;DR

This paper investigates the critical behavior of 3D Gross-Neveu and Higgs-Yukawa models, measuring and comparing their critical exponents through lattice simulations and epsilon-expansion, confirming their universality class equivalence.

Contribution

It provides the first lattice measurement of critical exponents for the 3D Gross-Neveu model and compares them with epsilon-expansion results for the Higgs-Yukawa model, establishing their universality.

Findings

Critical exponents for the Gross-Neveu model were measured and found consistent with the Higgs-Yukawa model.

The models' exponents agree within error margins, supporting their universality class equivalence.

The study confirms the models' critical behavior is consistent across different analytical and numerical methods.

Abstract

We measure the critical exponents of the three dimensional Gross-Neveu model with two four-component fermions. The exponents are inferred from the scaling behaviour of observables on different lattice sizes. We also calculate the exponents, through a second order epsilon-expansion around 4d, for the three dimensional Higgs-Yukawa model, which is expected to be in the same universality class and we find that the exponents agree. We conclude that the equivalence of the two models remains valid in 3d at fixed small N_f values.