Weak-coupling series and the critical indices ofZpspin systems in two dimensions

The quantum Hamiltonian version of $Z_p$ spin systems in two dimensions is used to study these model's weak-coupling phases. Twelve-term series are presented for the specific heats, magnetizations, and susceptibilities for $p=2, 3, 5, 6, \mathrm{and} 12$. Series analyses yield useful estimates of the critical indices for the three-state model. We suggest that the magnetization index $\beta$ lies within the interval 0.106-0.110. For $p>\mathrm{}4\mathrm{}$ the series indicate a phase transition below the self-dual point as predicted by Elitzur, Pearson, and Shigemitsu. The specific-heat series, however, show no anomaly at these points. Estimates of $\eta$ at the lower critical points are presented for $p=5, 6, \mathrm{and} 12$, and they agree with the expected result $\frac{4}{p^2}$.