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

• Published in: Nuclear physics. B 1994-03, Vol.415 (3), p.781-796
• Main Authors: Kärkkäinen, L., Lacaze, R., Lacock, P., Petersson, B.
• Format: Article
• Language: English
• Subjects: Critical point phenomena; Exact sciences and technology; Lattice theory and statistics (ising, potts, etc.); Phase transitions: general studies; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Thermodynamics
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(94)90309-3

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.