CRITICAL-BEHAVIOR OF THE 3-DIMENSIONAL GROSS-NEVEU AND HIGGS-YUKAWA MODELS

KARKKAINEN L, LACAZE R, LACOCK P, Petersson B. CRITICAL-BEHAVIOR OF THE 3-DIMENSIONAL GROSS-NEVEU AND HIGGS-YUKAWA MODELS. NUCLEAR PHYSICS B. 1994;415(3):781-796.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 nu = 1.00(4) and 2 - eta = gamma/nu = 1.246(8). We also calculate these exponents, through a second-order epsilon-expansion around four dimensions, for the three-dimensional Higgs-Yukawa model, which is expected to be in the same universality class, and obtain gamma/nu = 1.237 and nu = 0.948, while recent second-order 1/N(f) expansion calculations give gamma/nu = 1.256 and nu = 0.903. We conclude that the equivalence of the two models remains valid in three dimensions at fixed small N(f) values