THE SPECTRUM AND POTENTIAL IN LATTICE CP(N)

The two-dimensional CP(N) model is studied on the lattice. Cluster, local Metropolis and hybrid update schemes are used to study the low-lying spectrum and potential of the model for low and moderate values of N. A linearly confining potential is confirmed and accurate measurements of the adjoint bound state mass are obtained. The expected scaling is observed for this mass and for the topological susceptibility. Different forms of the action are shown to give similar results thus demonstrating universality. Little evidence is found for the expected singlet and higher bound states so the 1/N predictions for the spectrum can not be verified in detail. We independently confirm recent findings that critical slowing is not eliminated by the simplest cluster algorithms but find that a useful reduction in real autocorrelation times can be obtained using an efficiently vectorised hybrid of local and cluster update algorithms.