A finite size scaling analysis of the O(4)-invariant lattice φ4 theory

The critical behaviour of the three- and four-dimensional N=4 vector model is investigated by means of a Monte Carlo simulation on lattices with size between 43 and 163, and between 44 and 124, respectively. For obtaining information about some critical properties of the model, we use a method due to Binder which is based on the theory of finite size scaling. For the three-dimensional model we get estimates of the critical exponents ν and η which are compatible with estimates obtained from the ε-expansion. In four dimensions we study for two different values of the bare self-coupling λ (λ=1 in our normalization, and λ=∞) the scaling behaviour of some Green function ratios at the phase boundary. In both cases we find compatibility with the 'predicted' scaling behaviour at the gaussian fixed point. This is another independent numerical hint that the continuum limit of the four-dimensional O(4)-invariant lattice φ4-model is a free field theory. (orig.)