HAMILTONIAN FORMULATION OF THE MEAN SPHERICAL MODEL IN 1 + 1 DIMENSIONS

The exact spectrum of the mean spherical model in 1 + 1 dimensions is calculated using a lattice Hamiltonian formulation. This model is equivalent to the O(N) Heisenberg model in the limit N→, and exists only in a disordered phase. I investigate the singularity structure of the theory, and discuss implications for both weak- and strong-coupling approximations. I compare my results to approximate calculations for the O(3) and O(4) models by Hamer, Kogut, and Susskind, and find that the N→ limit reproduces many of their semiquantitative results concerning the transition from weak to strong coupling. © 1979 The American Physical Society.