Critical behaviour of the three-dimensional Gross-Neveu and Higgs-Yukawa models

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 lattice sizes 8 3, 12 3, 16 3, 24 3, and 32 3. We find that the model has a second-order phase transition with ν = 1.00(4) and 2 − η = γ/ ν = 1.246(8). We also calculate these exponents, through a second-order ϵ-expansion around four dimensions, for the three-dimensional Higgs-Yukawa model, which is expected to be in the same universality class, and obtain γ/ ν = 1.237 and ν = 0.948, while recent second-order 1/N ƒ expansion calculations give γ/ ν = 1.256 and ν = 0.903. We conclude that the equivalence of the two models remains valid in three dimensions at fixed small N ƒ values.