SU(N) × SU(N) spin systems in two dimensions crossover, variant actions and finite size scaling

Studies of the SU(3) × SU(3) chiral model with various actions are made in two dimensions using Monte Carlo methods. Similarities with four-dimensional gauge models are drawn and the relevance of topological excitations is seen in computer simulations. Finite size scaling studies of the fundamental model suggest that asymptotic freedom scaling laws are obscured by the rich phase structure in models with generalized actions. Actions which are adjusted to fit continuum forms more accurately at weak coupling may be necessary to extract quantitative physics of the continuum limit from such models. Similar procedures may be necessary for SU(3) gauge theory in four dimensions.