Study of Lambda hyperon parameters and crossover phenomena in SU(N) x SU(N) sigma models in two dimensions

The spin system anaogues of recent studies of the string tension and lambda parameters of SU(N) gauge theories in 4 dimensions are carried out for the SU(N) x SU(N) and O(N) models in 2 dimensions. The relations between the lambda parameters of both the Euclidean and Hamiltonian formulation of the lattice models and he lambda parameter of the continuum models are obtained. The one loop finite renormalization of the speed of light in the lattice Hamiltonian formulations of the O(N) and SU(N) x SU(N) models is calculated. Strong coupling calculations of the mass gaps of these spin models are done for all N and the constants of proportionally between the gap and the lambda parameter of the continuum models are obtained. These results are contrasted with similar calculations for the SU(N) gauge models in 3 + 1 dimensions. The numerical results suggest that the crossover from weak to strong coupling in the lattice O(N) models becomes less abrupt as N increases while the crossover for the SU(N) x SU(N) models becomes more abrupt.